Russian Deputy Foreign Minister Sergei Ryabkov said this "would be a very dangerous step" and accused the US of risking international condemnation in a bid for "total supremacy" in the military sphere.
He insisted that Moscow observed "in the strictest way" the three-decade-old Intermediate-Range Nuclear Forces Treaty, known as the INF, while accusing Washington of "flagrant violations."
The treaty was signed in 1987 by the then US president Ronald Reagan and Soviet leader Mikhail Gorbachev.
But Trump on Saturday claimed Russia had long violated it.
"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," he told reporters.
"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."
Ryabkov said Sunday he hoped Bolton would explain the US plans "more substantively and clearly."
The Trump administration has complained of Moscow's deployment of 9M729 missiles, which Washington says can travel more than 310 miles (500 kilometers), and thus violate the INF treaty.
The treaty, which banned missiles that could travel between 310 and 3,400 miles, resolved a crisis that had begun in the 1980s with the deployment of Soviet SS-20 nuclear-tipped, intermediate-range ballistic missiles targeting Western capitals.
A Russian foreign ministry official earlier accused Washington of implementing policy "toward dismantling the nuclear deal".
Washington "has approached this step over the course of many years by deliberately and step by step destroying the basis for the agreement," said the unnamed official, quoted by Russia's three main news agencies.
The official accused the US of backing out of international agreements that put it on an equal footing with other countries because it wanted to protect American "exceptionalism."
Russian Senator Alexei Pushkov wrote on Twitter that the move was "the second powerful blow against the whole system of strategic stability in the world" after Washington's 2001 withdrawal from the Anti-Ballistic Missile treaty.
"And again, the initiator of the dissolution of the agreement is the US," he added.
US withdrawal from the INF "will destroy any prospects of extending the New Start treaty," the head of the Russian senate's foreign affairs committee Konstantin Kosachev warned on Facebook.
Germany Foreign Minister Heiko Maas said the US should consider the consequences, both for Europe and for future disarmament efforts, of pulling out of the treaty.
"The treaty ... has for 30 years been an important pillar of our European security architecture," Maas said in a statement issued on Sunday. "We have often urged Russia to address serious allegations that it is violating the agreement. We now urge the US to consider the possible consequences."
AFP and Reuters contribured to this story.