Emerging from the meeting, Trump said the talk was a "very good start for everybody." The summit lasted more than two hours, longer than the 90 minutes that had originally been planned.
Earlier on Monday the president predicted that he and Putin would have an "extraordinary relationship" and that he is looking forward to their discussion.
Monday's highly anticipated meeting takes place in the wake of a contentious NATO summit, and only days after the U.S. Justice Department charged 12 Russian intelligence officers with hacking Democrats in an attempt to interfere with the 2016 election. That indictment includes the most detailed U.S. accusations yet that Moscow meddled in the election in favor of Trump.
Trump had insisted the two leaders meetearly in the day without any aides present — stirring concerns that Putin, a former KGB officer, will outflank his American counterpart.
Trump added it is important to improve the relationship between Washington and Moscow.
"I think we have great opportunities together as two countries that frankly have not been getting along very well for the last number of years," Trump said. "I really think the world wants to see us get along."
Trump also said because the U.S. and Russia are "the two great nuclear powers," they would have to discuss nuclear weapons. "We have 90 percent of the nuclear and that is not a good thing, that's a bad thing and I hope we can do something about that," Trump said.
In order to calm new fears of a budding arms race, Trump said he would discuss reducing nuclear weapons with Putin.
"If we can do something to substantially reduce them, I mean, ideally get rid of them, maybe that's a dream, but certainly it's a subject that I'll be bringing up with him," Trump said last week. "The proliferation is a tremendous, I mean, to me, it's the biggest problem in the world, nuclear weapons, biggest problem in the world."
One option Trump may present to Putin is a new nuclear weapons agreement. The New START treaty, which is the current nuke agreement, is slated to expire in 2021.
Meanwhile, Moscow has accelerated its development of hypersonic weapons, threats the U.S. is currently unable to defend against.
In March, the Russian leader touted his nation's hypersonic weapons as "invincible" during a state of the nation address.
"I want to tell all those who have fueled the arms race over the last 15 years, sought to win unilateral advantages over Russia, introduced unlawful sanctions aimed to contain our country's development: You have failed to contain Russia," Putin said during his address.
Of the six weapons Putin debuted in March, CNBC has learned that two of them will be ready for war by 2020, according to sources with direct knowledge of U.S. intelligence reports.