The Prime Minister said it is a “welcome sign” that a phone call between French leader Emmanuel Macron and the Russian president had shown Mr Putin may be “willing to engage in finding a diplomatic solution”.
Downing Street said the Prime Minister and Mr Macron agreed during a discussion on Sunday that the next week would be “crucial” in the bid to prevent an invasion of Ukraine.
It comes as the White House said US President Joe Biden has “accepted in principle” a meeting with Mr Putin as long as Russia holds off on any invasion plans.
Ukraine is currently surrounded on three sides by about 150,000 Russian soldiers, warplanes and equipment, with the West predicting that Moscow is poised to launch an offensive on Kyiv – a battle Mr Johnson has predicted would be “bloody and protracted”.
In a readout of the call between Mr Macron and Mr Putin, the Elysee Palace said the pair agreed to work towards a ceasefire in eastern Ukraine where violence has escalated between Ukrainian government forces and pro-Russian separatists.
French and Russian foreign ministers will meet in Paris to advance a solution to the current tensions, while the two heads of state “made a firm engagement to take all useful actions to avoid escalation, reduce risks and preserve peace”, according to a statement.
The Prime Minister, who has said a conflict between Kyiv and Moscow would amount to a war on a scale not seen since the Second World War, spoke to Mr Macron after the French president’s dealings with Mr Putin on Sunday.
A No 10 spokeswoman said: “The Prime Minister noted that President Putin’s commitments to President Macron were a welcome sign that he might still be willing to engage in finding a diplomatic solution.”
The leaders “underscored the need for President Putin to step back from his current threats and withdraw troops from Ukraine’s border”, Downing Street added.
Before the call, the Conservative Party leader had conceded that a joint US-UK sanction threat to prevent Russian state-linked firms from trading in pounds and dollars in the event of an incursion – a move he predicted would hit the Kremlin “very hard” – may “not be enough on its own” to prevent a conflict.
White House press secretary Jen Psaki said in a statement the US is “committed to pursuing diplomacy until the moment an invasion begins”, adding US secretary of state, Antony Blinken, and Russian foreign minister, Sergei Lavrov, are scheduled to meet in Europe later this week.
She said: “President Biden accepted in principle a meeting with President Putin following that engagement… if an invasion hasn’t happened.
“We are always ready for diplomacy. We are also ready to impose swift and severe consequences should Russia instead choose war.”
Western fears about an invasion grew after Russia and Belarus extended joint military exercises beyond the original intention to end them on Sunday.
It is feared the displays are a further indication that Russia, which is also conducting naval drills off the coast of the Black Sea, is gearing up for an offensive.
There are 7,000 more Russian troops on the Ukrainian border than there were a few days ago, a business minister has said.
Paul Scully told Sky News the number had been bolstered “despite the Russians trying to signal the fact they were pulling away from the border”.
He said: “So there is a very, very credible threat and that’s why we’ve got to continue to be vigilant, we’ve got to continue to work with Ukraine and Poland, as Liz Truss, the Foreign Secretary, was doing just this week.”
He warned “the loss of life will be horrendous” if Russian President Vladimir Putin does not engage in diplomacy.
Shelling in rebel-held areas of eastern Ukraine increased over the weekend, with the Prime Minister suggesting the activity was part of a Russian plan to invade.
Hundreds of artillery shells exploded along the contact line between the two sides in the Donetsk and Luhansk regions, and thousands of people were evacuated into Russia in a move some commentators believe is designed by Moscow to paint Kyiv as the aggressor.
There is anxiety that Russia, which also carried out nuclear drills on the weekend, could use the increase in tension as a pretext for an attack.
The Prime Minister said British intelligence had suggested that the surge in fighting bore “all the signs” that Mr Putin’s attack plan has “already in some senses begun”, Mr Johnson told the BBC.