Rubio claims 'tremendous amount of progress' in Ukraine peace talks following Geneva meeting

"We had a very good day today. I think we made a tremendous amount of progress, even from the last time I spoke to you," Rubio said.

"We began almost three weeks ago with a foundational document that we socialized and ran by both sides, and with input from both sides," he said.

"We arrived here today with one goal: to take what - it's 28 points or 26 points, depending on which version, as it continued to evolve and try to narrow the ones that were open items. And we have achieved that today in a very substantial way," he said.

The weekend talks centered on a 28-point plan, which is a framework drafted by the U.S. outlining steps for a possible ceasefire and political settlement.

The plan has reportedly evolved through several iterations, narrowing disputes point by point as both sides weigh concessions.

"Now, obviously, like any final agreement, it'll have to be agreed upon by the presidents, and there are a couple of issues that we need to continue to work on," Rubio clarified.

While declining to specify unresolved issues, Rubio described the moment as "delicate."

"This is a very delicate moment, and it's important - like I said, there's not agreement on those yet.  Some of it is semantics or language; others require higher-level decisions and consultation; others, I think, just need more time to work through," he said before touching on some issues.

"There were some that involved equities or the role of the EU or of NATO or so forth, and those we kind of segregated out because we just met with the national security advisors for various European countries, and those are things we'll have to discuss with them because it involves them."

"I don't want to declare victory or finality here. There's still some work to be done," he added.

Suggesting there is intent to ensure Ukraine's security, Rubio said that they all "recognize that part of getting a final end to this war will require for Ukraine to feel as if it is safe, and it is never going to be invaded or attacked again."

"The deadline is we want to get this done as soon as possible. Obviously, we'd love it to be Thursday," he added.