WASHINGTON (Reuters) -President Donald Trump reversed course on Friday and said Russia did in fact invade Ukraine, and that Kyiv would soon sign a minerals agreement with the United States as part of efforts to end the Ukraine war.

Trump had said on Tuesday that Ukraine "should have never started" the war three years ago, prompting a wave of criticism both domestically and internationally. Pressed on the subject in an interview with Fox News Radio on Friday, he acknowledged Russia had invaded Ukraine on the order of Russian President Vladimir Putin.

"Russia attacked, but they shouldn't have let him attack," Trump said, adding that Ukraine President Volodymyr Zelenskiy and then-U.S. President Joe Biden should have taken steps to avert the invasion.

Later, Trump predicted a minerals agreement would be reached soon.

"We're signing an agreement, hopefully in the next fairly short period of time," Trump told reporters in the Oval Office when asked about a possible deal for Ukraine's minerals.

Zelenskiy said separately on Friday that Ukrainian and U.S. teams were working on a draft agreement. "I am hoping for ... a fair result," he said in a video address after sharp exchanges this week between the two leaders.

Trump denounced Zelenskiy as a "dictator" on Wednesday and warned he had to move quickly to secure peace with Russia, which invaded Ukraine nearly three years ago, or risk losing his country.

The change in tone from the United States, Ukraine's most important backer, has alarmed European officials and stoked fears that Kyiv could be forced into a peace deal that favors Putin.

Zelenskiy had said Trump was trapped in a "disinformation bubble", but later toned down his statements and said he was hoping for American pragmatism.

Zelenskiy on Wednesday rejected U.S. demands for $500 billion in mineral wealth from Ukraine to repay Washington for wartime aid, saying the United States had supplied nowhere near that sum so far and offered no specific security guarantees in the agreement.

Ukraine has valuable deposits of strategic minerals that the U.S. wants. These include uranium, lithium, cobalt, rare earths and more and are used in applications such as batteries, technology and aerospace.

'THEY DON'T HAVE ANY CARDS'

Speaking at a White House event earlier on Friday, Trump was critical of Zelenskiy while refraining from negative comments about Putin.

"I've had very good talks with Putin, and I've had not such good talks with Ukraine," Trump said. "They don't have any cards, but they're playing tough."

Separately, the United States on Friday proposed a United Nations resolution to mark the third anniversary of Russia's invasion of Ukraine. The three-paragraph U.S. draft, seen by Reuters, mourns loss of life during the "Russia-Ukraine conflict" and "implores a swift end to the conflict."

Kyiv and its European allies want their own text to be adopted by the UN General Assembly on Monday calling for de-escalation, an early cessation of hostilities and peaceful resolution to the conflict.

The German government said on Friday that Chancellor Olaf Scholz and Zelenskiy agreed in a phone call that Ukraine must have a seat at the table in peace talks.

Polish President Andrzej Duda, meanwhile, urged Zelenskiy to keep up calm and constructive cooperation with Trump.

Duda, whose term in office expires this year, was one of Trump's preferred international partners during his 2017-2021 presidency and they have described themselves as friends.

Poland's president is due to meet Trump in Washington on Saturday, Poland's state news agency PAP reported.