The US president also said he would back European security guarantees for Ukraine as European leaders gathered for the extraordinary White House meeting.
"I think President Putin wants to find an answer, too," Trump told Zelenskiy and European leaders.
"And we'll see in a certain period of time, not very far from now, a week or two weeks, we're going to know whether or not we're going to solve this or is this horrible fighting going to continue."
Trump stopped short of committing US troops to a collective effort to bolster Ukraine's security.
He said instead that there would be a "NATO-like" security presence and that all those details would be hashed out with EU leaders.
"They want to give protection and they feel very strongly about it and we'll help them out with that," Trump said.
"I think its very important to get the deal done."
Trump's engagement with Zelenskiy had a strikingly different feel to their last Oval Office meeting in February.
It was a disastrous moment that led to Trump abruptly ending talks with the Ukrainian delegation, and temporarily pausing some aid for Kyiv, after he and Vice President JD Vance complained that Zelenskiy had shown insufficient gratitude for US military assistance.
Zelenskiy at the start of the meeting presented a letter from his wife, Olena Zelenska, for Trump's wife, Melania.
The US first lady over the weekend sent a letter to Putin urging him to consider the children impacted by the conflict and bring an end to the brutal 3.5 year war.
Trump at one point needled Zelenskiy over Ukraine delaying elections.
They had been scheduled for last year but were delayed because of the ongoing Russian invasion.
Ukrainian law does not allow presidential elections to be held when martial law is in effect.
Trump joked that a similar circumstance wouldn't play well in the US.
"So let me just say three and a half years from now — so you mean, if we happen to be in a war with somebody, no more elections, oh, I wonder what the fake news would say," Trump said.
Monday's hastily assembled meeting came after Trump met in Alaska on Friday with Putin.
Trump has said the onus is now on Zelenskiy to agree to concessions of land that he said could end the war.
Russia now controls roughly one-fifth of Ukrainian territory.
"If everything works out today, we'll have a trilat," Trump said, referring to possible three-way talks among Zelenskiy, Putin and Trump.
"We're going to work with Russia, we're going to work with Ukraine."
Trump said he plans to talk to Putin after his meetings with Zelenskiy and European leaders.
Zelenskiy expressed openness to trilateral talks.
After Trump held one-on-one talks with Zelenskiy, the two then gathered with European Commission President Ursula von der Leyen, French President Emmanuel Macron, British Prime Minister Keir Starmer, German Chancellor Friedrich Merz, Italian Premier Giorgia Meloni, Finnish President Alexander Stubb and NATO Secretary-General Mark Rutte.
The European leaders were left out of Trump's summit with Putin.
They want to safeguard Ukraine and the continent from any widening aggression from Moscow.
Many arrived at the White House with the explicit goal of protecting Ukraine's interests — a rare show of diplomatic force.
Putin opposes Ukraine joining NATO outright, yet Trump's team claims the Russian leader is open to Western allies agreeing to defend Ukraine if it comes under attack.
"Clearly there are no easy solutions when talking about ending a war and building peace," Meloni told reporters.
"We have to explore all possible solutions to guarantee peace, to guarantee justice, and to guarantee security for our countries."
European leaders suggested forging a temporary ceasefire is not off the table.
