U.S. President Donald Trump said that he had discussed nuclear arms control with Russian President Vladimir Putin at the summit in Alaska - and that China should be involved too - with the ultimate aim of "denuclearization".
What has Putin offered Trump on nuclear weapons and what might he offer?
PUTIN'S OFFER
Just a day before his meeting with Trump, Putin suggested that Moscow and Washington could reach a deal on nuclear arms control.
Russia, the United States and China are all undertaking major modernisations of their nuclear arsenals just as the last remaining nuclear arms control treaty - signed in an attempt to reduce the risk of nuclear war - is poised to expire.
Russia has about 4,300 stockpiled and deployed nuclear warheads and the United States has about 3,700, a total of about 87% of the world's total inventory, according to research by the Federation of American Scientists.
The New Strategic Arms Reduction Treaty, or New START, which caps the number of strategic nuclear warheads that the United States and Russia can deploy, and the deployment of land- and submarine-based missiles and bombers to deliver them, is due to run out on February 5, 2026.
The United States blames Russia for the collapse of Cold War agreements such as the 1972 Anti-Ballistic Missile Treaty and the 1987 Intermediate-Range Nuclear Forces Treaty.
The United States formally withdrew from the INF Treaty in 2019, citing Russian violations, which Moscow denied. The United States withdrew from the ABM Treaty in 2002.
Russia, which has said it would resume nuclear testing if the United States did, has also raised concerns about Trump's so-called "Golden Dome" missile defence shield.
CHINA TOO?
The United States has long wanted to involve China, the world's third largest nuclear power, in arms control but Beijing has so far resisted.
"China remains intent on modernizing, diversifying, and expanding its nuclear posture," according to the U.S. intelligence community's Annual Threat Assessment.
China is the world's third largest nuclear power with about 600 warheads, followed by France with 290, and Britain with 225, according to the Federation of American Scientists.
NUCLEAR THREATS
Both Putin and Trump have explicitly warned in public of the risk that World War Three could break out over Ukraine.
Putin last year lowered the threshold for a nuclear strike in Russia's nuclear doctrine, including a clause that it could consider a nuclear strike in response to a conventional attack on its territory.
Trump in August said he had ordered two nuclear submarines to be positioned in "the appropriate regions" in response to remarks from former Russian President Dmitry Medvedev about the risk of war between the nuclear-armed adversaries.
Putin has repeatedly cautioned the West that Moscow is not bluffing about being ready to use nuclear weapons if Russia were attacked.
The United States in 2022 was so concerned about the possible use of tactical nuclear weapons by Russia that it warned Putin over the consequences of using such weapons, according to Bill Burns, who was then director of the Central Intelligence Agency.
