"We didn't get there" on a ceasefire, Trump described. And yet there appears to be real momentum this time, coming out of Alaska.

Ukrainian President Zelensky is meanwhile set to arrive in Washington Monday to discuss peace in the Oval Office. Of course, talks didn't go so well last time - and there's likely to be persisting tensions - given that the conflict, as explained by Putin on Friday, would never have happened if Trump had been president, something which Trump himself has long asserted.

Trump had told European leaders in a post-summit call that he's now seeking a trilateral summit with Putin and Zelensky as soon as next Friday, according to sources in Axios. "I think the meeting was a 10," Trump said in a post-summit interview with Fox News. "In the sense, we got along great, and it's good when two big powers get along, especially when they're nuclear powers. We're No. 1 and they're No. 2 in the world."

And yet Putin's firm conditions make such a trilateral summit unlikely at such a near date - also given the Russian president has in the recent past made clear he would only meet with Zelensky if the two were ready to sign a deal, or essentially already at the goal line.

The Kremlin has still maintained that Zelensky doesn't have legal legitimacy, given the cancelation of elections in Ukraine and extension far past his term expiration.

According to more from Axios, this is where things stand in terms of Putin's demands, based on admin sources:

They said Putin had demanded that Ukraine cede two of the four regions to which Russia has laid claim (Donetsk and Luhansk), and freeze the front lines in the other two (Kherson and Zaporizhzhia). Russia controls nearly all of Luhansk, but only about three-quarters of Donetsk.

Putin presented his willingness to stop pushing forward in Kherson and Zaporizhzhia as a concession, in exchange for Ukraine withdrawing from Donetsk, one source briefed on the call said. In reality, Russia hasn't made any progress in those areas for some time.

A Ukrainian source said the U.S. side had the impression Putin was willing to negotiate over the small slivers of the Sumy and Kharkiv regions under Russian control.