Ukrainian President Volodymyr Zelenskyy says he and his US counterpart Donald Trump made "great achievements" while discussing a 20-point plan to end the war with Russia.
However, Mr Trump said there were one or two "thorny issues" that remained.
He has been hosting Mr Zelenskyy at Mar-a-Lago to discuss the finer points of a peace plan put forward by Washington.
Mr Zelenskyy told reporters after the meeting that a security guarantee between the two countries as part of the deal was "100 per cent agreed", while Mr Trump said it was almost completely agreed.
"Our teams will continue working on all aspects [of the peace plan]," Mr Zelenskyy said.
The pair said they had spoken to a number of their European counterparts, as well as NATO and the EU leaders following their meeting, with Mr Trump set to host all parties in the coming weeks to "finalise all discussed matters".
"We agreed that security guarantees [are] the key milestone in achieving lasting peace," Mr Zelenskyy said.
"And Ukraine is ready for peace."
Mr Trump said some land in Ukraine may be "up for grabs" as part of the peace process.
A key aspect of discussions now is the establishment of a "special economic zone" in the Donbas.
The US leader said that part was unresolved, but that progress had been made.
Mr Trump said Ukraine should look to make a land deal before it lost more territory in the future.
"Some of that land has been taken, some of that land is maybe up for grabs but it may be taken over the next period of a number of months, and you're better off making a deal now," he said.
"Look let me tell you they have been very brave. They've fought very hard and continue to fight very hard."
Hurdles to a peace deal remain
Mr Trump held a call with Russian President Vladimir Putin shortly before the Mar-a-Lago meeting, suggesting there were still obstacles to peace.
Mr Trump told reporters he would call Mr Putin again following the meeting with Mr Zelenskyy.
Mr Trump described his earlier call as "productive", while Kremlin foreign policy aide Yuri Ushakov said it was "friendly".
Mr Ushakov, in Moscow, said Mr Putin told Mr Trump a 60-day ceasefire proposed by the European Union and Ukraine would prolong the war.
The Kremlin aide also said Ukraine needed to make a quick decision about land in the Donbas.
Mr Zelenskyy has said he hopes to soften a US proposal for Ukrainian forces to withdraw completely from the Donbas region of eastern Ukraine, a Russian demand that would mean ceding some territory held by Ukrainian forces.
It comes as three guided aerial bombs launched by Russia struck private homes in the eastern city of Sloviansk overnight, local time, according to the head of the local military administration, Vadym Lakh.
Three people were injured and one man died, Mr Lakh said in a post on the Telegram messenger app.
Russia attacked Ukraine's capital with ballistic missiles and drones the previous day, killing at least one person and wounding 27, Ukrainian authorities said.
Mr Trump said, however, that he still believed Mr Putin was "very serious" about ending the war, saying he believed Ukraine had also made "some very strong attacks".
"And I don't say that negatively. I think, you probably have to," Mr Trump told reporters as Mr Zelenskyy stood by his side following their meeting.
Mr Trump also said it was possible that the peace negotiations would fall apart.
He said: "In a few weeks, we will know one way or the other, I think. … But it could also go poorly."
