Mr Pushkov made the troubling comments during an interview with the state-controlled Tass Russian News Agency.
He said: “The danger is that the United States is pushing the world to another Cuban Missile Crisis.
“Back then we were lucky to avoid an exchange of nuclear strikes.
“Only God knows what all this may end up in now.”
Trump has announced the US will pull out of the Intermediate-Range Nuclear Forces Treaty (INF), which was established between the US and the Soviet Union in 1987.
The treaty prohibits the development of nuclear missiles with a range of between 500 and 5,000 kilometres.
The US claims Russia is breaching the agreement by continuing to work on mid-range ballistic missiles which could carry nuclear warheads.
There is particular focus on the 9M729 intermediate missile system, which Russia insists does not violate the INF treaty.
Mr Pushkov’s criticism was echoed by former Soviet leader Mikhail Gorbachev, who signed the INF treaty along with President Reagan in 1987.
He described the decision as a “mistake” and the product of a questionable mind.
Last week, the US President told reporters in Washington: “I’m terminating the agreement because they violated the agreement.”
Asked whether the move was meant as a threat to Russian President Vladimir Putin, Mr Pushkov replied: “It’s a threat to whoever you want.
“And it includes China, it includes Russia and it includes anyone else that wants to play that game.”
Mr Pushkov is a member of the Russian Senate and chairman of its temporary commission on information policy.
Despite the US’s rhetoric, the Trump administration is yet to start the formal withdrawal process from the INF treaty.
In 2002, President George W Bush withdrew the US from the Anti-Ballistic Missile Treaty, thus allowing the country to develop a defensive missile shield.
John Bolton, Trump’s national security advisor and an advocate of withdrawing from the INF treaty, was involved in these negotiations.