"I don't think his mind has changed at all. I think ultimately, if this whole effort doesn't work out, then there is going to have to be additional consequences to Russia. But we're trying to avoid that by reaching a peace agreement," Rubio told ABC News' "This Week" co-anchor Martha Raddatz.
"We're not at the precipice of a peace agreement. We're not at the edge of one. But I do think progress was made," he continued.
Rubio suggested that both sides will have to make concessions.
"You can't have a peace agreement unless both sides give and get. You can't have a peace agreement unless both sides make concessions," Rubio said. "If not, it's just called surrender, and neither side is going to surrender, so both sides are going to have to make concessions."
On those concessions, Rubio said, "Of course, concessions were asked, but what utility would there be of me going on a program and tell you, 'We've wagged our finger at Putin and told him, "You must do this," and "you must do that."' It's gonna make -- it's only going to make it harder."
"The deadline is as soon as possible. We want this war to end as soon as possible. I mean, that's why we're working on in terms of sanctions. Look, at the end of the day, if we can't reach a peace agreement here and this war continues and so forth, then I anticipate you'll see the president take further action," he continued.
Trump had said before the summit that he wanted a ceasefire and for the killing to stop and there would be consequences if it didn't.
"Ultimately, at the end of the day, we have to get the Russian side to agree to things that they don't want to agree to if we're going to have peace. If not, they'll just be a war. They'll keep killing each other, and life will go on in America and in the rest of the world, but not for Ukraine," he said.
Rubio stressed that a peace agreement can't be achieved if only one side is involved in the talks and it's the United States objective to bring both nations together.
"You're not going to reach a ceasefire or a peace agreement in a meeting in which only one side is represented. That's why it's important to bring both leaders together, and that's the goal here," Rubio said.
Rubio said that details of Trump's meeting with Putin will not be disclosed.
"These peace agreements and negotiations -- they don't work when they're conducted in the media, either through leaks or through lies," Rubio said.
On Monday, Ukrainian President Volodymyr Zelenskyy will travel to the White House to meet with Trump. He will be accompanied by several other European leaders.
