Trump says Moscow has violated the terms of the weapons pact, which dates to 1987, but he offered no further details on Saturday afternoon.
President Vladimir Putin says should there be a nuclear attack, Russians will go to heaven as martyrs because they would be victims of an "aggression".
Earlier this month, U.S. Defense Secretary Jim Mattis said Russia's violation of the INF treaty was "untenable" and, unless it changed course, the United States would respond.
"But if Russia's doing it and if China's doing it, and we're adhering to the agreement, that's unacceptable". China is not now party to the pact.
The comments come as United States national security adviser John Bolton was set to travel to Russia, Azerbaijan, Armenia and Georgia on Saturday.
The agreement has constrained the USA from developing new weapons, but America will begin developing them unless Russian Federation and China agree not to possess or develop the weapons, Trump said.
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.
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There was no immediate comment from the Kremlin or the Russian Foreign Ministry on Trump's announcement.
President Trump reiterated his discontent with the current situation.
More than 500,000 people have been killed in the seven-year-long war, mostly at the regime's hands.
Speaking in the Black Sea resort city of Sochi, Putin said the hostages included several USA and European nationals, Reuters reports.
American officials previously accused Moscow of violating the treaty by deploying a land-based cruise missile in a show of force against NATO.
Balsamo reported from Washington.
Putin made the claims Thursday during the Valdai forum in the Black Sea resort city of Sochi, saying IS had taken 700 people from a displaced persons camp near Deir el-Zour in an area controlled by US -backed forces.