"Under my administration, we will never apologize for advancing America's interests," Trump told US lawmakers assembled in the House chamber.
"Perhaps we can negotiate a different agreement, adding China and others. Or perhaps we can't - in which case, we will outspend and out-innovate all others by far," Trump said.
While pointing the finger at Russia, US officials have voiced concern that the 1987 treaty does not constrain China, whose rapidly growing military relies on medium-range missiles as a core part of its defence strategy.
The INF treaty banned all missiles with a range of 500 to 5,500 kilometres (310 to 3,400 miles), a legacy of the end of the Cold War as last Soviet leader Mikhail Gorbachev and US president Ronald Reagan sought to ease European fears of an arms race that would destroy their cities.
Russian President Vladimir Putin - who has sought a warm relationship with Trump but is widely reviled by the US establishment -- responded Saturday by saying Moscow would also leave the INF treaty.
Defense Minister Sergei Shoigu said earlier Tuesday that Putin had approved plans for new missiles.
"During 2019-2020 we have to develop a land-based version of the seaborne Kalibr system equipped with a long range cruise missile which showed good results in Syria," Shoigu told defence officials.
"Over the same period we will also have to create a land-based missile system with a long-range hypersonic missile," he said.
Latvia urges international pact
Foreign Minister Edgars Rinkevics of Latvia - for which former ruler Russia looms large as a threat - voiced hope that Washington and Moscow would work with other powers on a new agreement.
"I would advocate - even if it is going to take a very long period of time, even if it may be a very, sometimes, complex and disappointing, from time to time, process - it would be good to try to find a way forward on a multilateral arms control agreement in this area," Rinkevics told AFP.
"It needs to be more than the United States and Russia because there are more countries that can produce such weapons than 30 years ago," he said in an interview in Washington, where he is taking part in a 79-member conference Wednesday on the fight against the Islamic State group.
Latvia, like other members of the NATO alliance, has backed the United States which has charged since the administration of former president Barack Obama that Russia is infringing on the INF treaty with the range of its new 9M729 missile system.
But Rinkevics played down the immediate impact of the INF treaty's demise, saying that Russia had already been stepping up military movements since Moscow's 2014 annexation of Crimea.
He acknowledged that a future pact was unlikely to be as sweeping as the INF treaty.
The United States last week started the process of exiting the Intermediate-Range Nuclear Forces (INF) Treaty, saying that Russia has been violating the pact through a new missile system and ignored repeated complaints.