British Prime Minister Boris Johnson and Russian President Vladimir Putin agreed in a phone call on Wednesday to work towards a "peaceful resolution" of the crisis over Ukraine, according to Downing Street.

"The leaders agreed that aggravation was in no one's interest," it said in a statement, adding that Johnson had warned Putin that any Russian invasion would be a "tragic miscalculation".

Both leaders noted existing dialogue between their governments over issues including climate change, Afghanistan and the Iran nuclear deal, it said.

"They agreed to apply this spirit of dialogue to the current tensions in order to find a peaceful resolution."

Johnson also stressed that Ukraine had every right to apply to join the "defensive alliance" of NATO if it wished, and that Kyiv should be included in any talks over the standoff with Russia.

The prime minister visited Kyiv on Tuesday, warning after talks with Ukraine's President Volodymyr Zelensky that Russian forces massed on the border represented a "clear and present danger" to Ukraine.

Britain said at the weekend that it was preparing to offer NATO a "major" deployment of troops, weapons, warships and jets in Europe amid the tensions.

The offer could see London double the approximately 1,150 UK troops currently in eastern European countries and "defensive weapons" sent to Estonia, along with anti-tank missiles given to Ukraine.