Joe Biden hailed “a good day” for democracy after Democrats defied history and outperformed expectations in America’s midterm elections, leaving control of Congress on a knife-edge.

With ballots still being counted, Democrats were hopeful about holding the Senate, though the outcome of the tight races in Arizona and Nevada were still uncertain on Wednesday evening and another key race in Georgia was headed to a runoff. Democrats need to win two of those seats to maintain Senate control.

Republicans, meanwhile, felt they were on course to win the House – but by a much narrower margin than widely predicted.

“We had an election yesterday – it was a good day, I think, for democracy,” Biden told reporters at the White House. “And I think it was a good day for America.”

The president added: “While the press and the pundits are predicting a giant red wave, it didn’t happen … Democrats had a strong night.”

Biden looked poised for the best midterm performance by an incumbent president’s party since George W Bush in 2002. Perhaps the biggest loser of the night was his predecessor, Donald Trump, as many of his handpicked candidates slumped to defeat, throwing fresh doubt over his political future.

The party that controls the White House typically loses seats in midterm elections and opinion polls had shown broad dissatisfaction with Biden and the economy. The conditions appeared ripe for a so-called Republican “red wave” that could have drowned the president’s legislative agenda.

But it did not turn out that way and a day that had been expected to dawn with Democratic soul-searching was instead filled with Republican finger-pointing and recriminations.

“The Republican party needs to do a really deep introspection look in the mirror right now because this is an absolute disaster,” Marc Thiessen, a former chief speechwriter for Bush, told Fox News.

The results of the most hotly contested Senate races were giving many Republicans heartburn. Biden campaigned hard in Pennsylvania, the state of his birth, and was rewarded when John Fetterman, the lieutenant governor who suffered a stroke during the campaign, defeated Mehmet Oz, a celebrity doctor endorsed by Trump.

Senator Mark Kelly maintained a lead over the Republican Blake Masters in Arizona, though Kelly’s colleague from Nevada, Catherine Cortez Masto, had fallen behind. But hundreds of thousands of ballots remain uncounted in those races, and election officials have warned it could take days to determine the winners.

In Georgia, Senator Raphael Warnock, a pastor, and Republican challenger Herschel Walker, a former American football star, are headed to a 6 December runoff, a race that could determine control of the chamber. The Alaska Senate race was also still too close to call, but the top two candidates are both Republicans.

Republicans had been heavily favoured to take the House and did claim a major prize, winning the New York seat of Sean Patrick Maloney, the head of the Democrats’ campaign arm.

But the widespread gains many forecasters predicted failed to materialise. Vulnerable Democrats such as Abigail Spanberger of Virginia and Elissa Slotkin of Michigan held on, keeping the party’s hopes of House control alive hours after polls closed.

It may be days before the House results are clear, with roughly 30 critical races still pending, including several key battles in California; although the state is overall Democratic, there are five competitive races where votes are still being counted and where party affiliation could flip.

The House speaker, Nancy Pelosi, expressed optimism in the early hours of Wednesday.

“While many races remain too close to call, it is clear that House Democratic members and candidates are strongly outperforming expectations across the country,” Pelosi said. “As states continue to tabulate the final results, every vote must be counted as cast.”

Kevin McCarthy, the Republican minority leader, appeared at 1.59am, much later than expected, at an event in Washington. He declared: “It is clear we are going to take the House back.”

McCarthy later announced his bid to become speaker if Republicans do win the House. But with a wafer-thin majority, he could face political headaches as pro-Trump extremists seek to dominate the agenda.

Biden said he would speak to McCarthy later in the day. He told reporters: “I’m prepared to work with my Republican colleagues. The American people have made clear, I think, that they expect the Republicans to be prepared to work with me as well.”

The results also brought welcome news for abortion rights supporters devastated by the supreme court’s reversal of Roe v Wade in June. California, Vermont and Michigan voted to strengthen abortion rights into their constitutions, while conservative states Kentucky and Montana rejected measures to restrict access to the procedure.

Early exit polls suggested abortion rights had been a motivating factor for many voters, despite predictions the issue would be overshadowed by economic concerns. One exit poll conducted by Edison Research found that 27% of voters named abortion as their top priority, compared to 31% who said the same of inflation.

Threats to democracy also appeared to be weighing heavily on voters’ minds. According to AP VoteCast, 44% said the future of democracy was their primary consideration, making it the second-most common response behind inflation.

Overall, the night shaped up poorly for election deniers and candidates endorsed by Trump. Although dozens of incumbents who challenged the 2020 presidential result did win, election deniers in key gubernatorial and secretary of state races were on track for defeat.

Democrats won governors’ races in Michigan, Wisconsin and Pennsylvania, crucial battlegrounds in recent presidential elections likely to be pivotal again in 2024. Many saw it as yet another rebuke of Trump and his “Make America great again” (Maga) movement following losses in 2018 and 2020.

Ezra Levin, co-founder and co-executive director of Indivisible, said: “This was supposed to be Maga’s triumphant night. It turned into a massive embarrassment. While we’re still awaiting final results, the overall picture is clear: Democrats massively performed the midterm fundamentals. Voters don’t like anti-abortion zealots. Voters don’t like election deniers. Voters don’t like Trump. And voters don’t like Maga.”

As Trump-endorsed candidates fell, others downplayed their connection to the former president. JD Vance, who won the Ohio Republican Senate primary largely thanks to Trump’s endorsement, did not mention his name while delivering a victory speech on Tuesday.

The results reportedly infuriated Trump, who is expected to announce another presidential campaign as early as next week. Even more worrisome for him, the Florida governor, Ron DeSantis, frequently named as a potential presidential candidate, easily cruised to re-election.

DeSantis’s 19-point victory in Trump’s home state – notably carrying largely Latino counties such as Miami-Dade and Osceola – only intensified chatter about 2024.

In a potential sign of trouble for Trump, the New York Post, which the former president has been known to read avidly, put a photo of DeSantis on its cover. “DeFuture”, the cover’s headline read. “Young GOP star DeSantis romps to victory in Florida.”

The glowing coverage is sure to irritate Trump, who is famous for lashing out against fellow Republicans who steal the spotlight and who last week branded the governor “Ron DeSanctimonious”.

In a preview of a potentially bloody primary, Trump told Fox News: “I think if he runs, he could hurt himself very badly. I really believe he could hurt himself badly. I would tell you things about him that won’t be very flattering – I know more about him than anybody – other than, perhaps, his wife.”

Biden, meanwhile, suggested that he is likely to make a final decision on running early next year with input from his wife, Jill Biden.

“Our intention is to run again,” he said, in the White House state dining room. “That’s been our intention, regardless of what the outcome of this election was.”