Donald Trump left more questions than answers on Friday as he claimed “great progress” in his high-stakes summit with Vladimir Putin but admitted that no deal had been reached to end Russia’s war on Ukraine.

The US president also suggested that it was now up to Volodymyr Zelenskyy to “get it done” and that a meeting would be set up between the Ukrainian president and Putin, which Trump might attend.

“We had an extremely productive meeting and many points were agreed to,” Trump said at a joint press conference in Anchorage, Alaska. “There are just a very few that are left. Some are not that significant. One is probably the most significant but we have a very good chance of getting there.”

He cautioned: “There’s no deal until there’s a deal.”

The two leaders lavished praise on each other – Putin endorsed Trump’s view that the war would never have started if Trump had won the 2020 election – but offered no details of the nearly three-hour meeting and took no questions from reporters.

Putin, speaking through an interpreter, described Trump’s efforts on Ukraine as “precious” and, suggested the two leaders had hammered out “an understanding”. He urged Europe to “not throw a wrench in the works” and to “not use backroom dealings” to torpedo it.

Putin said that he agreed that Ukraine’s security must be guaranteed – but also said that the “root causes” of the conflict must be resolved. Those “root causes” have previously included his demands for Ukraine’s formal renunciation of Nato membership as well as its “denazification” – a vague set of demands that in practice amount to the removal of Zelenskyy.

Zelenskyy and European allies may have been alarmed by Trump’s body language and deferential attitude toward Putin, whom he welcomed warmly at an Alaska air force base and allowed to ride in the presidential limousine known as “the beast”.

Trump told reporters: “We really made some great progress today. I’ve always had a fantastic relationship with President Putin – with Vladimir.”

As the press conference ended Putin suggested their next meeting might take place in Moscow, and dozens of reporters shouted questions in vain. The US president, who can typically never resist a free-wheeling press conference, left the stage without answering any of them.

However, he did elaborate in an interview with Sean Hannity, a host on the conservative Fox News network, suggesting that the ball was in Ukraine’s court. “Now it’s really up to President Zelenskyy to get it done and I would also say the European nations – they have to get involved a little bit.

“They’re going to set up a meeting now between President Zelenskyy and President Putin and myself I guess. I didn’t ask about it. Not that I want to be there but I want to make sure it gets done and we have a pretty good chance of getting it done.”

The Senate Democratic leader, Chuck Schumer, said Trump had “rolled out the red carpet” for an “authoritarian thug … instead of standing with our allies”.

“While we wait for critical details of what was discussed – on first take it appears Trump handed Putin legitimacy, a global stage, zero accountability, and got nothing in return. Our fear is that this wasn’t diplomacy – it was just theatre.”

Ken Martin, chair of the Democratic National Committee, said: “Donald Trump has been cozying up to Vladimir Putin for years, and this meeting underscored the depth of his sick obsession with the Russian dictator and accused war criminal.”

He added: “Trump has been clear that his foreign policy agenda is letting Russia ‘do whatever the hell they want’ – no matter how disastrous for the US and our allies – and when put to the test, Trump embarrassed the United States by folding like a cheap suit.”

The two leaders disembarked their planes at 11.08am local time at Joint Base Elmendorf-Richardson, a cold war-era air force base on the outskirts of Anchorage, Alaska.

The friendly, tactile body language that followed offered a stark contrast to Trump’s shakedown of Zelenskyy, in the Oval Office in February.

Trump and Putin walked down red carpets that had been rolled up to their respective planes and met where the carpets came to a T, with Trump arriving first and clapping as Putin approached.

The men shared a warm handshake and what appeared to be some lighthearted banter. Trump gave Putin a friendly tap on the arm. Putin grinned and pointed skyward while their hands were still clasped.

The pair walked together towards a platform bearing a sign that read Alaska 2025 as B-2s and F-22s – military aircraft designed to oppose Russia during the cold war – flew over to mark the moment.