The three-decade-old Intermediate-Range Nuclear Forces Treaty, known as the INF, was signed in 1987 by president Ronald Reagan.
"We're the ones who have stayed in the agreement and we've honored the agreement, but Russia has not unfortunately honored the agreement, so we're going to terminate the agreement and we're going to pull out," Trump told reporters in Elko, Nevada.
"Russia has violated the agreement. They've been violating it for many years. I don't know why president (Barack) Obama didn't negotiate or pull out. And we're not going to let them violate a nuclear agreement and go out and do weapons (while) we're not allowed to."
Trump spoke as his National Security Advisor John Bolton was in Moscow to meet with Russia's Foreign Minister Sergei Lavrov, ahead of what is expected to be a second summit between Trump and Russian leader Vladimir Putin this year.
US-Russia ties are under deep strain over accusations that Moscow meddled in the 2016 presidential election, as well as tension over Russian support for the Syrian government in the country's civil war, and the conflict in Ukraine.
However, Washington is looking for support from Moscow in finding resolutions to the Syria war and putting pressure on both Iran and North Korea.
No new summit between Trump and Putin has been announced, but one is expected in the near future.
The two leaders will be in Paris on November 11 to attend commemorations marking the end of World War I.
A senior Trump administration official, who spoke on condition of anonymity, said another potential date would be when the presidents both attend the Group of 20 meeting on November 30 to December 1.
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