The New Start agreement, limiting both sides' strategic nuclear arsenals, expires in early 2021.
Commenting on Bolton's demand that Moscow pressure Iran into getting its troops out of Syria, Paul said that while this was a "reasonable request", it should rather apply to "any foreign nation that has troops in Syria that haven't been invited".
However, in describing USA objectives in Syria, Bolton said nothing about the Geneva talks.
Patrushev told RIA Novosti that continuing contacts with the United States military was "particularly important" for Moscow.
"We're not going to solve Syria here", he said.
Bolton said that he also warned his Russian counterpart not to intervene the upcoming US midterm elections, saying that he made it clear the USA wouldn't tolerate election meddling in 2018 and they were prepared to "take necessary steps to prevent it from happening".
Bolton said he and his counterpart covered an array of topics, including nuclear nonproliferation, arms control, counterterrorism, illegal immigration, cyber-related issues, and "regional issues" including Syria, the broader Middle East, Afghanistan, and Ukraine.
Grammy-Winning Country Star Gretchen Wilson Arrested at Connecticut Airport
Wilson was flying into Bradley International Airport in Windsor Locks Monday evening when cops were dispatched to the airport. Gretchen Wilson attends the 50th annual CMA Awards at the Bridgestone Arena on November 2016 in Nashville.
Iran and Russian Federation are two leading backers of Syrian President Bashar Assad.
"I think we made a lot of progress, we identified certain areas where lines of communication could be restored and more work done by the affected agencies - State Dept, Defense Department, other agencies as well", Bolton said.
Bolton said that contrary to reports that have suggested Moscow has agreed to distance Iranian forces some 40 to 80 kilometers from Israel's border, recent talks between the United States and Russian Federation on the matter concerned "the complete return of both regular and irregular Iranian forces".
US National Security Adviser John Bolton said on Wednesday that Washington was not seeking to oust Iran's leadership and that renewed sanctions were having a stronger impact on Tehran than anticipated.
President Donald Trump's hawkish national security adviser says the Europeans have to make a choice between the U.S. and Iran in observing American sanctions which he claims have been more effective than expected.
Russian Foreign Minister Sergei Lavrov responded to USA defense official John Bolton's threats against the Syrian government by demanding all uninvited foreign forces leave Syria.
U.S. President Donald Trump met Russian President Vladimir Putin last month, an event Moscow quickly chalked up as a triumph. The White House later denied Trump was unaware of the terms of the treaty.
Bolton insisted that recent USA political turmoil over guilty pleas and verdicts against by former Trump campaign chairman Paul Manafort and Trump's former personal lawyer, Michael Cohen - "doesn't have any effect" on his job.
"Of course not", Bolton said.