Ahead of the summit on Friday, Trump greeted the Russian leader on a red carpet on the tarmac at a US military base.
The two shook hands warmly and touched each other on the arm before riding in Trump's limo to the summit site nearby.
The two leaders sat silently with their respective delegations seated to the side in their first meeting since 2019.
They were seated in front of a blue backdrop that had the words, "Pursuing Peace" printed on it.
Ukrainian President Volodymyr Zelenskiy, who was not invited to the talks, and his European allies fear Trump might sell out Ukraine by essentially freezing the conflict and recognising, if only informally, Russian control over one-fifth of Ukraine.
Earlier, Trump sought to assuage such concerns, saying he would let Ukraine decide on any possible territorial swaps.
"I'm not here to negotiate for Ukraine, I'm here to get them at a table," he said.
Asked what would make the meeting a success, he told reporters: "I want to see a ceasefire rapidly... I'm not going to be happy if it's not today... I want the killing to stop."
Trump will be joined in his meeting with Putin by Secretary of State Marco Rubio and Trump's special envoy to Russia, Steve Witkoff, White House spokeswoman Karoline Leavitt said.
The Russian officials accompanying Putin in the talks with the US delegation will be foreign policy aide Yury Ushakov and Foreign Minister Sergei Lavrov.
Both the US and Russian presidents are seeking wins from their first face-to-face talks since Trump returned to the White House.
Trump, who casts the war as a "bloodbath", is pressing for a truce in the 3.5-year-old war that would bolster his credentials as a global peacemaker worthy of the Nobel Peace Prize.
For Putin, the summit is already a big win as he can use it to say that years of Western attempts to isolate Russia have unravelled and that Moscow has retaken its rightful place at the top table of international diplomacy.
Russian special envoy Kirill Dmitriev described the pre-summit mood as "combative" and said the two leaders would discuss not only Ukraine but the full spectrum of bilateral relations, Russia's RIA news agency reported.
Trump, who once said he would end Russia's war in Ukraine within 24 hours, conceded on Thursday it had proven a tougher nut to crack than he thought.
Trump said that if talks went well, quickly arranging a second three-way summit with Zelenskiy would be even more important than his encounter with Putin.
Zelenskiy said Russia was continuing to attack Ukraine ahead of a summit.
"On the day of the negotiations, they also kill people. And that says a lot," Zelenskiy said on the Telegram messaging app.
Earlier, Ukrainian regional officials said Russia had launched a ballistic missile into Dnipropetrovsk region in eastern Ukraine, killing one person and wounding at least one other.
One source acquainted with Kremlin thinking said there were signs Moscow could be ready to strike a compromise on Ukraine, given that Putin understood Russia's economic vulnerability and costs of continuing the war.
Putin has said he is open to a full ceasefire but that issues of verification must first be sorted out.
One compromise could be a truce in the air war.
Ukrainians who spoke to Reuters in central Kyiv on Friday were not optimistic about the Alaska summit.
"Nothing good will happen there, because war is war, it will not end. The territories - we're not going to give anything to anyone," said Tetiana Harkavenko, a 65-year-old cleaner.
