Mr Gorbachev was one of the original signatories to the Intermediate-Range Nuclear Forces (INF) Treaty, signed originally in 1987 with then-US President Ronald Reagan.
“Under no circumstances should we tear up old disarmament agreements. ... Do they really not understand in Washington what this could lead to?,” Mr Gorbachev said to Interfax news agency.
"Russia has not, unfortunately, honoured the agreement so we're going to terminate the agreement and we're going to pull out," he told journalists.
He did not provide evidence of what Moscow had done to prompt the decision to withdraw from the treaty which prohibits both countries from holding or testing ground-launched cruise missiles with a range between 300 and 3,400 miles (500 and 5,500 km).
US authorities have said Russia has developed a ground-launched system in violation of the treaty but Moscow has denied the accusation.
“We’re not going to let them violate a nuclear agreement and go out and do weapons and we’re not allowed to,” Mr Trump 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 lets none of us develop[s] those weapons, but if Russia’s doing it and if China’s doing it, and we’re adhering to the agreement, that’s unacceptable," he said, echoing his statements about several bilateral and multilateral treaties of which the US was part.
A Kremlin spokesman said Russian President Vladimir Putin would seek answers about the planned withdrawal when he meets US National Security Advisor John Bolton who is scheduled to travel to Moscow this week.
Russian Deputy Foreign Minister Sergei Ryabkov echoed Mr Gorbachev's comments as well, calling Mr Trump's announcement "very dangerous".
According to news agency RIA, he also warned there may some sort of "military-technical" retaliation though did not specify what that could be.
German Foreign Minister Heiko Maas said that for 30 years the INF treaty had been a pillar of Europe's security architecture. He said in a statement: "We now urge the United States to consider the possible consequences," of quitting the pact.
Not everyone thought Mr Trump's decision to withdraw from yet another nuclear treaty - the last was the historic 2015 deal with Iran which had provided some sanctions relief to Tehran in exchange for stopping development of its weapons system.
UK Defence Secretary Gavin Williamson, who is in the US as the Royal Navy aircraft carrier HMS Elizabeth visits New York, said: “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".
He accused Russia of "making a mockery" of the INF treaty and advised Moscow to “get its house in order”.
Mr Williamson said: “We of course want to see this treaty continue to stand but it does require two parties to be committed to it and at the moment you have one party that is ignoring it.”
On 4 October, US Defence Secretary James Mattis had set the stage for the withdrawal during a meeting at the North Atlantic Treaty Organisation (Nato) in Brussels, the 29-member body set up for mutual defence against attacks.
Mr Trump caused shock waves among members last year when he suggested a membership be extended to Russia.
Moscow's continued deployment of nuclear-capable missiles is "untenable" and will require one of several options of response from the US and other countries.
“Russia must return to compliance with the [1987 Intermediate-range Nuclear Forces Treaty] or the US will need to match its capabilities to protect US and NATO interests," Mr Mattis said.
The US Ambassador to Nato, Kay Bailey Hutchinson, had earlier said if Moscow continues to be in non-compliance of the treaty then the US would need to look to ways to "take out" the weapons system.
Ms Hutchinson said the US does not itself want to violate the INF treaty, but indicated Russia could somehow compel it to do so.
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