Both Jens Stoltenberg and US Secretary of State Mike Pompeo have blamed Russia for the Cold War treaty's collapse.
Nato and the US accuse Russia of violating the pact by deploying a new type of missile, which Russia denies.
The Intermediate-Range Nuclear Force banned missiles with ranges between 500 and 5,500km (310-3,400 miles).
The INF treaty was signed by US President Ronald Reagan and Soviet leader Mikhail Gorbachev in 1987 but its collapse more than 30 years later has raised fears of a news arms race.
Why has it ended?
Last year the Americans said they had evidence that the new Russian cruise missiles fall within the range banned by the treaty.
Accusations about the 9M729 missiles - known to Nato as SSC-8 - were then put to Washington's Nato allies, which all backed the US claim.
In February, President Donald Trump set the 2 August deadline for the US to withdraw from the pact if Russia didn't come into compliance.
Image captionRussia's new 9M729 missile worries the US and its allies
Russian President Vladimir Putin suspended his country's own obligations to the treaty shortly afterwards.
"Russia is solely responsible for the treaty's demise," Secretary of State Mike Pompeo said in a statement on Friday.
"With the full support of our Nato allies, the United States has determined Russia to be in material breach of the treaty, and has subsequently suspended our obligations under the treaty," he added.
Russia's foreign ministry confirmed the INF treaty had been terminated "at the initiative of the US", in a statement carried by the official Ria news agency.
What are the risks?
Nato Secretary General Jens Stoltenberg said the transatlantic alliance would "respond in a measured and responsible way to the significant risks posed by the Russian 9M729 missile to allied security".
But, he added, Nato "does not want a new arms race" and confirmed there were no plans for the alliance to deploy land-based nuclear missiles of its own in Europe.
Last month, he told the BBC that the Russian missiles were nuclear-capable,mobile, very hard to detect and could reach European cities within minutes.
"This is serious," he added. "The INF treaty has been a cornerstone in arms control for decades, and now we see the demise of the treaty."
UN Secretary General Antonio Guterres has warned that "an invaluable brake on nuclear war" was being lost.
"This will likely heighten, not reduce, the threat posed by ballistic missiles," he added, urging all parties to "seek agreement on a new common path for international arms control".
Analysts fear that the collapse of the historic agreement could lead to a new arms race between the US, Russia and China.
"Now that the treaty is over, we will see the development and deployment of new weapons," Pavel Felgenhauer, a Russian military analyst, told AFP news agency. "Russia is already ready."
What is the Intermediate-Range Nuclear Forces (INF) treaty?
Soviet leader Mikhail Gorbachev and US President Ronald Reagan signed the treaty in 1987
Signed by the US and the USSR in 1987, the arms control deal banned all nuclear and non-nuclear missiles with short and medium ranges, except sea-launched weapons
The US had been concerned by the Soviet deployment of the SS-20 missile system in 1979 and responded by placing Pershing and cruise missiles in Europe - sparking widespread protests
By 1991, nearly 2,700 missiles had been destroyed
The two countries were allowed to inspect each other's installations
The demise of the INF treaty - the only disarmament agreement ever to eliminate a whole category of nuclear weapons - represents a significant setback for advocates of arms control.
That it comes at a time when the US is increasingly concerned by the threat from what it sees as a resurgent Russia is doubly unsettling.
Neither Moscow nor Washington appears to value such treaties.
The most important agreement of the old Cold War years - the New Start treaty - that limits long-range nuclear weapons is set to expire in February 2021. Its survival is far from certain.
The paradox is that arms control appeared unimportant after the collapse of the Soviet Union when tensions were low.
Now that they are mounting again, disarmament agreements could have an important part to play in maintaining stability.
Instead arms control is in crisis, just when dangerous new weapons technologies (involving artificial intelligence and high-speed "hypersonic" missiles) are being developed.
Where did things go wrong?
In 2007, Russian President Vladimir Putin declared the treaty no longer served Russia's interests.
That happened after US President George W Bush, in 2002, pulled the US out of the Anti-Ballistic Missile Treaty, which banned weapons designed to counter ballistic nuclear missiles.
In 2014, then US President Barack Obama accused Russia of breaching the INF Treaty after it allegedly tested a ground-launched cruise missile.
Russia strongly denies building missiles that violate the accord
He reportedly chose not to withdraw from the treaty under pressure from European leaders, who said such a move could restart an arms race.
Then last year, Nato supported the US accusations and formally accused Russia of breaking the treaty.
Russia denied the accusation and President Putin said it was a pretext for the US to leave the pact.
Amid worsening ties between Washington and Moscow, Turkey last month received the first parts of a Russian S-400 missile defence system despite opposition from the US.
The US has warned that Turkey cannot have both the S-400 anti-aircraft defence system and US F-35 fighter jets.
Turkey and the US are Nato allies but Turkey has also been establishing closer links with Russia.