Russian efforts to disrupt the American presidential election in 2016 remain a source of tension between the two nations and has led to US sanctions of several Russians close to Putin and his circle. The election meddling has also the focus of the investigation by Special Counsel Robert Mueller, who has been looking into whether any Trump associates colluded in the Russian efforts.

Putin and Trump spoke briefly at the Asia-Pacific Economic Cooperation summit in Vietnam last November, and had two encounters during the G-20 summit in Germany last July.

A Trump-Russia summit could potentially echo a historic Cold War meeting in Austria between a newly elected President John F. Kennedy and the Soviet leader Nikita Khrushchev. Kennedy and Khrushchev met at a historic summit in Vienna in 1961, shortly after the US-backed invasion of Cuba's Bay of Pigs and amid tensions between the superpowers over Berlin.

Third world war

The White House's leak on the possiblity of a summit comes as Putin warned that a third world war "would lead to the end of civilisation" as he accused America of violating the nuclear balance.

Responding to a worried viewer during a televised phone-in, Putin called for new arms control negotiations and quoted Albert Einstein's aphorism that "World War IV will be fought with sticks and stones".

He said Russia had developed weapons to breach US missile defences after Washington left the Soviet-era anti-ballistic missile treaty in 2002. "The fear of mutually assured destruction has always restrained and forced military powers to respect each other," he said. "This is on the understanding that a third world war would lead to the end of civilisation."

He added: "The exit of the United States from the missile defence treaty was an attempt to ruin this parity, but our efforts in the development of new weapons will preserve the parity."

Nuclear weapons, including an underwater drone and a hypersonic glider warhead, prompted fears of a new arms race when the Russian leader announced them in March. US intelligence said Moscow's nuclear-powered hypersonic cruise missile with "unlimited" range had crashed in tests.

Putin argued that Russia had proved doubters wrong by developing weapons such as the Avant-Garde missile, which flies 20 times faster than the speed of sound. The Mach-10 Dagger missile and a laser weapon were already in service, he said.

The Cold War rhetoric continued as Mr Putin likened Western sanctions on Russia to the US containment policy against the USSR. He also cited Soviet successes in the space race while pledging to launch 600 new satellites and develop a super-heavy rocket.

He briefly touched on next week's World Cup, saying that stadiums built in 11 Russian cities should not become white elephants but help "develop a new generation of football players".

During the annual show, which ran for more than four hours, Mr Putin answered 73 questions out of more than 2 million submitted by the country's people. The annual event is carefully stage-managed, although a few uncomfortable questions popped up on screens showing submissions in real time.

"Why is there money for tanks, bombs, planes and machine guns in this country, but not for people?" read one, but the presenters ignored it.

Mr Putin also brushed off London's assertion that Sergei Skripal, the former double agent, and his daughter Yulia, were poisoned in Salisbury with a Novichok military-grade nerve agent.

Contrary to the findings of the Organisation for the Prohibition of Chemical Weapons, he insisted a lesser quality poison must have been used and demanded Moscow's officials be allowed to take part in the investigation.

Asked about the Syria conflict, Mr Putin said Russia had ceased combat missions but would keep troops there "as long as it's advantageous".

The call-in show allows Mr Putin to give answers to issues like rising fuel prices, flooded homes or underfunded hospitals, while passing on the blame to his underlings.

In a first, ministers and the heads of the country's 85 regions had to wait nervously on camera for the duration in case the president called on them.

Bloomberg, Telegraph, London