By Frederik Pleitgen and Mary Ilyushina, CNN

(CNN) -- Russia understands why the United States wants to withdraw from a 30-year-old nuclear non-proliferation treaty, US National Security Adviser John Bolton told CNN.

"I think they understand our reasons quite clearly, some of which I think they might fully appreciate from their own strategic perspective," Bolton told CNN.

"I think their preference is that they have stayed in this and we do not withdraw, but we are giving them the reasons why we are going do it."

Bolton spoke to reporters in Moscow on Tuesday morning after laying flowers at the place where Russian opposition leader Boris Nemtsov was killed.

Speaking at a news conference later Tuesday, Bolton said he had a lengthy discussion with Russian President Vladimir Putin about Trump's intention to exit INF treaty.

He said there had been "six years of Russian non-compliance" of the treaty which Russia denies.

Bolton also said the treaty was a "Cold War bilateral agreement" but we are now in a "multi-polar world" and we need to reflect this "new reality."

Trump announced on Saturday that the US will withdraw from the Intermediate-Range Nuclear Forces Treaty (INF), a 31-year-old nuclear weapons pact between the countries.

The INF was signed by President Ronald Reagan and Soviet Union leader Mikhail Gorbachev in 1987, when the two superpowers were trying to end the Cold War.

The announcement triggered strong criticism from arms control advocates, who say Trump is removing an important safeguard and could trigger a new and dangerous arms race.

Asked by CNN if the conversations and atmosphere during his visit have been constructive, Bolton said: "I think we have had very professional, very work-like conversations and we look forward to continuing that," he said.

"Technology has changed, your strategic reality has changed, and we both have to deal with it," he said.

Bolton met with Russian Defense Minister Sergei Shoigu and Putin on Tuesday.

He said the decision to withdraw from the INF treaty "recognizes the changed reality."

"I think given Russian violations of the treaty as well, you can't rely on teleology, we have to rely on the facts on the ground," he added.

Earlier Tuesday, Shoigu told Bolton that Moscow and Washington could solve a number of world problems if they worked together, according to state-run news agency RIA Novosti.

"This concerns both the strategic issues of nuclear deterrence, and, of course, issues of resolving major longstanding conflicts," said Shoigu, according to the news agency.

"I am sure that even small steps will benefit our relations and help restore trust," he added.

Tuesday is Bolton's second day in Moscow. On Monday, Bolton met with the head of Russia's National Security Council, Nikolai Patrushev, and later dined with Foreign Minister Sergey Lavrov.

Russia's foreign ministry later tweeted photographs of the US delegation in Moscow.