US Secretary of State Antony Blinken issued a pledge on Sunday to increase pressure on Russia through sanctions and provide more aid to Ukraine, but warned that Russia held a military advantage that western allies are finding hard to counter and the war was set to last “some time”.

“Vladimir Putin has, unfortunately, the capacity with the sheer manpower he has in Ukraine and overmatch he has, the ability to keep grinding things down against incredibly resilient and courageous Ukrainians. I think we have to be prepared for this to last for some time,” Blinken told CNN.

America’s top diplomat was speaking from Chisinau in Moldova, which sits between Romania, a member of the North Atlantic Treaty Organization (Nato) military alliance, and the south-western border of Ukraine on the Black Sea, not far from the Ukrainian city of Odesa which is threatened by advancing Russian forces.

Blinken has spent the weekend visiting Nato member nations in eastern Europe that have taken in refugees from Ukraine. He said of the destruction being perpetrated under the direction of Russian president Vladimir Putin in the south-eastern Ukrainian city of Mariupol that: “Just winning a battle is not winning a war, and just taking a city does not mean taking the hearts and minds of the Ukrainian people. On the contrary, he is destined to lose.”

“The Ukrainian people will not allow themselves to be subjugated to Vladimir Putin or to Russia’s rule – but it could take some time, and meanwhile the suffering is real and it’s terrible,” he told CNN’s State of the Union Sunday morning TV show.

Blinken said he’d met with refugees fleeing the Russian invasion of Ukraine, currently estimated at a stunning 1.5 million.

“We’re doing everything we can to bring this to an end as quickly as we can but this may still go on for a while,” he added.

Pressed on US sanctions on Russia, Blinken defended Washington’s comparative lag in application compared to European Union allies and its failure to cut off Russian imports of oil by the US.

“We’re adding to sanctions virtually every day,” Blinken said. He said he had spoken to US president Joe Biden on Saturday and members of the cabinet on the issue of oil.

“We are now talking to our European partners and allies to look in a co-ordinated way at the prospect of banning Russian oil while making sure there is an appropriate supply of oil on world markets.”

Blinken also reacted to the issue of providing increased military aid to Ukraine, including sending US fighter jets to Poland so that that country can send supplies of used Migs and Sukhoi military planes to Ukraine, where the military is familiar with those Russian-style jets rather than western-made fighters.

“We are working with Poland to see if we can backfill anything they provide to Ukraine. We very much support them, providing planes that the Ukrainians can fly. But we also want to see if we can be helpful in making sure that whatever they provide to the Ukrainians, something goes to them to make up for any gap in security for Poland.”

But Blinken, on NBC, insisted that while the US would continue to add to Ukraine with “security assistance” – totaling more than $1bn over the past year – the US would not enforce a Ukrainian no fly zone or put the US in “direct conflict” with Russia.

“For everything we’re doing for Ukraine, the president also has a responsibility to not get us into a direct conflict, a direct war, with Russia, a nuclear power, and risk a war that expands beyond Ukraine to Europe. We’re trying to end this war in Ukraine, not start a larger one,” he said.

The White House issued a report of Joe Biden’s call with Ukrainian president Volodymyr Zelenskiy on Saturday evening, saying his administration is “surging security, humanitarian, and economic assistance to Ukraine and is working closely with Congress to secure additional funding”.

Lawmakers in a video call with Zelenskiy on Saturday morning said they were eager to approve an additional $10bn in spending to aid Ukraine.

Leaders are also accusing Vladimir Putin of suspected war crimes based on Russia’s blatant killing of Ukrainian civilians as part of its action, destroying residential areas far from likely military targets and also directly firing on civilians trying to evacuate.

“We have some very credible reports of attacks on civilians, which is what is considered a war crime.” Blinken said.

Republican senator Marco Rubio, vice chair of the Senate intelligence committee, said he thought the Russian people would ultimately remove Putin from power over his action in Ukraine.

“Hopefully to stand trial for war crimes, for what he has done,” Rubio said. He described Putin as “a monster” on ABC.

European Commission president Ursula von der Leyen said on Sunday morning on the same CNN show that an investigation is needed into whether Russia is committing war crimes in Ukraine.

“I think there needs to be a strong and clear investigation on this question,” she said.

US ambassador to the United Nations, Linda Thomas-Greenfield told ABC’s This Week: “Any attack on civilians is a war crime.”

Meanwhile, Ukraine is not willing to compromise on its territorial integrity in talks with Russia but is open to discussing “non- Nato models” for its future security, in a wider forum, one of its negotiators told Fox News.

Ukraine has pursued membership of Nato, cited by Putin as evidence of what he portrays as Nato aggression toward Russia.

Nato members “are not ready to even discuss having us in Nato, not for the next period of five or 10 years,” negotiator David Arakhamia said in remarks published on the Fox News website late on Saturday.

“We are ready to discuss some non-Nato models. For example, there could be direct guarantees by different countries like the US, China, UK, maybe Germany and France. We are open to discussing such things in a broader circle.”

And on Sunday afternoon, retired army general David Petraeus, former head of US central command during the conflicts in Iraq and Afghanistan, said he did not accept military assumptions that Kyiv will inevitably fall to Russia.

Russian forces have a 40-mile-long convoy of military vehicles stalled on the approach to the Ukrainian capital and Petraeus said it appeared “they cannot keep their columns fueled” and praised Ukrainian resilience so far.

“They’ve taken down road signs or pointed “Welcome to Hell” and stuff like that,” Petraeus told CNN.

“This is going to be a very long fight in Kyiv. The locals there have been stockpiling food, there is going to be an enormously fierce resistance. I don’t accept assumptions that it will fall,” he said.

Petraeus also noted Kyiv’s extensive surface area as a major obstacle for the Russian military, pointing out that the capital is spread across around 320 sq miles, larger than New York City and a little over half the size of London’s sprawl.