Nuclear arsenals are expanding around the world in a reversal of the gradual disarmament since the end of the Cold War.
The US and Russia put more of their nuclear stockpiles into operational deployment in 2020, a report said.
Meanwhile, the UK, China, India, Pakistan and North Korea are all in the process of expanding or upgrading their weapons systems.
“The overall number of warheads in global military stockpiles now appears to be increasing,” said Hans M. Kristensen, a senior fellow at the Stockholm International Peace Research Institute.
He said it was a “worrisome sign that the declining trend that has characterised global nuclear arsenals since the end of the Cold War has stalled”.
The Sipri report said about 3,800 nuclear weapons were deployed with operational forces, an increase since last year.
About 2,000 warheads were in a state of “high operational alert”, most of them belonging to the US or Russia.
Washington and Moscow agreed in January to extend New Start, their last remaining nuclear arms control treaty.
But Mr Kristensen said the prospects were poor for further agreements between the two former Cold War superpowers.
Nato Secretary General Jens Stoltenberg said at a summit on Monday that the alliance's relationship with Russia was at its lowest point since the Cold War.
The summit ended with a warning that Russia had “continued to diversify its nuclear arsenal” as it replaces Soviet-era missiles with new weapons.
US President Joe Biden will meet Russian President Vladimir Putin in Switzerland on Wednesday.
While the US and Russia dismantled some retired weapons last year, both are thought to have dozens more warheads in deployment.
“Both Russia and the US appear to be increasing the importance they attribute to nuclear weapons in their national security strategies,” Mr Kristensen said.
In March, Britain said that a cap of 180 nuclear warheads was "no longer possible" because of increasing global threats. The limit will be raised to 260.
The UK plans to maintain four nuclear-armed submarines and keep one on patrol at all times, in a policy of continuous deterrence which has been in place since 1969.
Concern over China's plans
China’s nuclear expansion prompted concern from Nato leaders, who toughened their stance on Beijing at Monday’s summit.
Nato described China for the first time as posing “systemic challenges” to the Western alliance.
China is rapidly expanding its nuclear arsenal and pursuing a “nuclear triad” of land, air and sea-based weapons, it is believed.
It has an inventory of about 350 warheads, Sipri said, an increase of 30 on last year.
The institute said India and Pakistan appeared to be expanding their nuclear arsenals, while North Korea continued to develop missiles.
It said there was a growing divide between nuclear-armed states upgrading their systems and countries seeking disarmament.
Nations without a nuclear stockpile were “impatient to see progress on nuclear disarmament”, it said.
The Nato summit was the first for Mr Biden, who assured allies of Washington's support after the rocky years of the Donald Trump presidency.
"We have Russia that is not acting in a way that is consistent with what we had hoped, as well as China," he said.
Nato leaders would “keep consulting closely” on nuclear deterrence and arms control, he said.