Donald Trump, the former US president, tried to get his spluttering White House bid off the launchpad on Saturday, declaring himself “more angry” than ever as he became the first candidate to hit the 2024 election campaign trail.

Trump swung through New Hampshire, which holds the first-in-the-nation Republican primary, and South Carolina, looking to shake off concerns about a lacklustre campaign and “Trump fatigue” among voters.

“We need a president who’s ready to hit the ground running on day one and boy, am I hitting the ground,” he told the New Hampshire state Republican party’s annual meeting. “They [the media] said, ‘He’s not doing rallies! He’s not campaigning! Maybe he’s lost that step.’ I’m more angry now and I’m more committed now than I ever was.” The remark elicited applause and cheers from the audience.

Trump formally launched his run for the White House more than two months ago with an address at his Mar-a-Lago club in Florida that was widely derided for its absence of sparkle or swagger.

Such is the humbling nature of America’s primary system that on Saturday the one time president, who used to fly in luxury on Air Force One with the world’s most awesome military at his disposal, found himself speaking from a rudimentary wooden lectern at a high school auditorium in Salem.

Later he introduced his South Carolina campaign leadership team at the state capitol in Columbia, an unusual choice for a man who first ran for office as anti-establishment outsider pledging to drain the swamp.

Both events contrasted sharply with the rollicking rallies in which Trump tends to thrive, suggesting an effort to show Republicans that he can be a more disciplined and conventional politician when he chooses. Newsmax, a conservative TV network, described his performances as “measured” and “presidential” – timeworn adjectives likely to have many Americans rolling their eyes after four years of tumult in the White House culminating in the deadly January 6 insurrection at the US Capitol.

But some things about Trump, now 76, don’t change. He entered the New Hampshire event to the sound of singer Lee Greenwood’s “God Bless the USA” and began with his customary dubious claim that there were thousands of people outside the packed venue. He quickly mocked Democrats with nicknames such as “Crazy” Nancy Pelosi and “Cryin’” Chuck Schumer.

Despite the advice of many Republicans to move on from his “big lie” that the 2020 election was stolen from him, he could not resist an early swipe. “As someone who’s won the New Hampshire presidential primary not once but twice, and by the way, I believe we also won two general elections, OK, if you want to know the truth, and I believe it very strongly in plenty of other places also.”

The remark prompted some approving whoops from the audience. Trump went on to tick off familiar subjects and dust off old anecdotes, from energy independence to Hunter Biden’s laptop. “We’re going Marxist,” he said, before decrying the participation of transgender people in women’s sports. He championed “gas stoves” and “gas cars” over their electric counterparts.

Some opinion polls have shown Trump more vulnerable among Republicans than any time since 2015, with Ron DeSantis, the governor of Florida, emerging as his principal rival. But the former president casually denied that he faces serious competition in the primary. “We are so far ahead in the polls … We’re gonna win and we’re gonna win very big.”

Later, in Columbia, Trump announced that South Carolina governor Henry McMaster would lead his campaign in the state. The ex-president was joined on stage by McMaster, frequent golf partner Senator Lindsey Graham and other team members including Congressman Joe Wilson, who in 2009 heckled President Barack Obama during a speech by shouting “You lie!”

Wilson was widely condemned at the time but Trump said on Saturday: “That voice was so beautiful as you called it out in Congress, Congressman Joe Wilson. I thought it was brilliant. See, that was done from the heart, that was done from the heart. I don’t know if you know it or not – you took a little heat at the time – people loved you for that because it showed honesty, dedication and love of your country.”

Speaking to around 500 people, Trump cut loose on red meat issues, promising to restore “election integrity” and stop an “invasion” at the southern border. He claimed without evidence that the true number of people crossing it could be 15m, many from “prisons” and “mental institutions”.

He then echoed the infamous campaign launch speech in June 2015 in which he alleged that Mexico was sending drugs, crime and rapists across the border. Without specifying Mexico this time, he said: “They’re sending people that are killers, murderers, they’re sending rapists and they’re sending frankly terrorists or terrorists are coming on their own and we can’t allow this to happen.”

DeSantis has made political capital from “culture wars” issues in Florida, picking fights with corporations such as Disney and forcing teachers to remove books from classrooms. Trump sought to show he will not be outdone on that turf.

To enthusiastic clapping and cheering, he said: “We’re going to stop the leftwing radical racists and perverts who are trying to indoctrinate our youth and we’re going to get their Marxist hands off of our children. We’re going to defeat the cult of gender ideology and reaffirm that God created two genders called men and women. We’re not going to allow men to play in women’s sports.”

Trump also claimed that America is “at the brink of world war three” and that, if he were president, he would have a peace deal between Russia and Ukraine negotiated in 24 hours. “That deal is waiting to be done but there’s nobody to do it,” he said.

At both campaign stops Trump tried a bizarre riff on the idea that every day in America is like “April Fools’ Day”, with borders open when they should be closed, Democrats opposing voter ID, the military going “woke”, men competing in women’s sports and America begging other nations for oil instead of using its own. “It’s supposed to be the opposite. April Fools’, right?”

New Hampshire and South Carolina are seen as potential kingmakers since they are among the first to hold their nominating contests. In New Hampshire, Republican Governor Chris Sununu has said he is having conversations about a primary bid, while in South Carolina, Senator Tim Scott is seen as a potential contender.

Rick Wilson, a cofounder of the Lincoln Project, an anti-Trump group, believes that Saturday’s events will put pressure on rival candidates to show their hand. “Trump knows that and because of that sense they’re missing the boat, that sense the base will start paying attention to Trump again, you see Kristi Noem attacking Ron DeSantis and Nikki Haley making noises on Fox and all these other not so subtle pre-game signals of what’s to come.”

Wilson added: “All the other candidates that want to be president on the Republican side have to build from scratch. They all have to start at zero. They all have to build up a campaign organisation, a staff, a team. They all lack a certain degree of name recognition and star power. Even DeSantis is not a well known quantity outside of a very narrow circle of Republican mega-donors. As we watch this whole thing shamble into position, you will see Trump being able to start to roll up some of these early states.”

Wilson remains convinced that Trump will win the Republican nomination. “That will not be a great thing for the party or for the other people but with the structural strengths that he has with the base – and a bunch of other candidates in the race dividing up the non-Trump vote – it’s over before it starts. We’re going to end up with a with a less exciting primary than people think.”

But there are unique uncertainties around the unique situation of a twice impeached one-term president trying to win back the White House. Frank Luntz, a pollster who has advised numerous Republican campaigns, takes the opposite view from Wilson: he believes that Trump is all washed up.

“How much Trump has fallen is a big deal and how much DeSantis has gained is a big deal,” Luntz said. “DeSantis is so far ahead of where Barack Obama was against Hillary Clinton [in the Democratic primary in 2007] because that’s the closest parallel.”

He predicts that DeSantis will be the Republican nominee in 2024. “I used to think that Trump was the prohibitive favourite but, now that he’s below 50% and the first vote is still a year away, he’s bleeding support.

“I talk to Trump people. We did a focus group on him a few weeks ago. They all still appreciate all that he did. They still think he was one of the greatest presidents in American history. But there’s too much drama and too much controversy and they’ve had enough. The conclusion from them is: Mr Trump, thank you for your service, this country is grateful, but it’s time to move on.”