The US says it has seen no indication Russia has moved nuclear weapons to neighbouring Belarus.
The EU's foreign policy chief Josep Borrell has cautioned Belarus about allowing Russia to station tactical nuclear weapons on its territory.
Borrell tweeted: “Belarus hosting Russian nuclear weapons would mean an irresponsible escalation & threat to European security. Belarus can still stop it, it is their choice. The EU stands ready to respond with further sanctions.”
In an interview on Saturday, Russian President Vladimir Putin said the move was triggered by Britain’s decision last week to provide Ukraine with armour-piercing rounds containing depleted uranium.
Tactical nuclear weapons are intended for use on the battlefield. They have a short range and a low yield compared with much more powerful nuclear warheads fitted to long-range missiles.
The move also drew swift condemnation from NATO spokesperson Oana Lungescu, who called it "dangerous and irresponsible".
The US says there has been no indication Russia has moved nuclear weapons across its border.
"We have not seen any reason to adjust our own strategic nuclear posture," the US Defense Department said in a statement.
On Sunday, Ukraine called for an urgent meeting of the UN Security Council, with Ukrainian Security Council Secretary Oleksiy Danilov saying the Kremlin had taken Belarus "nuclear hostage".
It is a "step towards the internal destabilisation of the country," he added.
Putin said Russia planned to maintain control over the nukes it sends to Belarus, with the construction of storage facilities to be completed by 1 July.
He didn’t say how many nuclear weapons Russia would keep in Belarus, which shares a long border with Ukraine and NATO members Poland, Lithuania and Latvia.
The US government believes Russia has about 2,000 tactical nuclear weapons, including bombs that can be carried by tactical aircraft, warheads for short-range missiles and artillery rounds.
Putin argued that by deploying its tactical nuclear weapons in Belarus, Russia was following the lead of the United States, noting the country has nukes in Belgium, Germany, Italy, the Netherlands and Turkey.
“We are doing what they have been doing for decades, stationing them in certain allied countries, preparing the launch platforms and training their crews,” Putin said, speaking in an interview on state television that aired Saturday night.
“We are going to do the same thing.”
The Russian leader claimed the move would not violate existing nuclear-non-proliferation agreements.
Russia currently stores tactical nuclear weapons at dedicated depots on its territory.
Moving part of the arsenal to a storage facility in Belarus would up the ante in the Ukrainian conflict by placing them closer to the combat zone and NATO states.
This will be the first time Moscow has based nuclear weapons outside of its borders.
Before the collapse of the Soviet Union in 1991, it stationed nukes in Ukraine, Belarus and Kazakhstan. However, they were transferred back to Russian territories in 1996.
For more information, watch Euronews' report in the video above.