The 1987 Intermediate-Range Nuclear Forces Treaty helps protect the security of the US and its allies in Europe and the Far East.
Negotiated by then US president Ronald Reagan and Soviet leader Mikhail Gorbachev, the Cold War-era treaty prohibits the US and Russia from possessing, producing or test-firing a ground-launched cruise missile with a range of 300 to 3,400 miles.
Mr Trump made the announcement during a campaign stop in Elko, Nevada, on Saturday.
He said: “Russia has not adhered to the agreement. So we are going to terminate the agreement.
“Russia has violated the agreement. They’ve been violating it for many years. I don’t know why President 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.”
A Russian foreign ministry official, quoted by three news agencies, responded by saying that Washington’s “main motive is a dream of a unipolar world”, one that will not be realised.
A Russian foreign ministry official 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”, the official said, quoted by Russia’s three main news agencies.
“This decision is part of the US policy course to withdraw from those international legal agreements that place equal responsibilities on it and its partners and make vulnerable its concept of its own ‘exceptionalism’.”
Mr Trump said the agreement had stopped the US developing new weapons but that they could soon start doing so – unless Russia and China agree not to possess or develop weapons.
China is not yet signed up to the pact.
The US leader said: “We’ll have to develop those weapons, unless Russia comes to us and China comes to us and they all come to us and say ‘let’s really get smart and let’s none of us develop those weapons’.
“But if Russia’s doing it and if China’s doing it, and we’re adhering to the agreement, that’s unacceptable.”
The comments come as US national security adviser John Bolton was set to travel to Russia, Azerbaijan, Armenia and Georgia on Saturday.
He will stop in Moscow first as tensions continue to grow with Russia over war in Syria, Ukraine and alleged Russian meddling in the 2016 presidential elections.
American officials previously accused Moscow of violating the treaty by deploying a land-based cruise missile that could allow it to launch a nuclear strike on Europe at short notice.
Russia has consistently denied any such violation and claimed US missile defences violate the agreement.
Mr Trump reiterated his discontent with the current situation.
He added: “If they get smart and if others get smart and they say ‘let’s not develop these horrible nuclear weapons’, I would be extremely happy with that, but as long as somebody’s violating the agreement, we’re not going to be the only ones to adhere to it.”
The UK Defence Secretary Gavin Williamson said Britain stands “absolutely resolute” with the US, and called on the Kremlin to “get its house in order”.
He told the Financial Times: “Our close and long-term ally of course is the United States and we will be absolutely resolute with the United States in hammering home a clear message that Russia needs to respect the treaty obligation that it signed.”