And while they discussed security concerns, the Pentagon warned that Russia is continuing to add "sizeable" troops along the Ukraine border, with a spokesman saying that with each passing day, Mr Putin is giving himself more military options.

In Moscow, President Macron said there needs to be a useful response for Ukraine. Putin, in turn, hailed France's role in shaping European security.

"I realise that we share concern about what's going on in Europe in the security sphere," Mr Putin said.

Mr Macron called for de-escalation as he sat down for the talks, adding: "Dialogue is necessary because that's the only thing that will help, in my view, to build a context of a security and stability on the European continent."

Putin's spokesman, Dmitry Peskov, described the visit as "very important," but sought to temper expectations, saying "the situation is too complex to expect a decisive breakthrough after just one meeting".

Mr Macron, who heads to Ukraine on Tuesday, spoke with US President Joe Biden on Sunday about the "ongoing diplomatic and deterrence efforts," according to the White House.

'Real and profound consequences' warns US

Speaking on Monday, US secretary of state Antony Blinken warned: "There will be real and profound consequences should Russia choose to continue aggression.

"We developed a high impact quick action response that would inflict massive costs on the Russian economy and financial system."

Actions, he said, would include sanctions and export controls that would "deny Russia the technology it needs in key sectors".

He said the US was working with Europe to also protect the energy supply, adding: "When energy supplies fail, economies falter".

German Chancellor Olaf Scholz is in Washington to meet US President Joe Biden as talks take place on both sides of the Atlantic to try to find a diplomatic solution to the crisis.

A delegation of senior US officials are heading to Europe this week, to discuss coordination of potential sanctions in the event of a Russian attack. Treasury, State, and Commerce department officials will travel to the UK, France, and Belgium to meet with counterparts as the US prepares punitive actions if Russia crosses into Ukraine.

'Russia does not want Ukraine'

"The geopolitical objective of Russia today is clearly not Ukraine, but to clarify the rules of cohabitation with NATO and the EU," Mr Macron said in an interview with French newspaper Journal du Dimanche on Sunday, ahead of his meeting in Moscow.

He added: "The security and sovereignty of Ukraine or any other European state cannot be a subject for compromise, while it is also legitimate for Russia to pose the question of its own security."

But, speaking to reporters in France, the French leader admitted: "I'm very worried by the situation on the ground."

Mr Macron's visit comes less than three months before France's presidential election - and he has yet to announce whether he will run.

According to sources close to Mr Macron, the aim of his visit is to buy time and freeze the situation for several months, at least until a "Super April" of elections in Europe - in Hungary, Slovenia and, crucially for the French leader, in France.

Read: West and Russia wage information war over Ukraine

'Heading to Putin's lair'

Over the past week, Mr Macron has made a frenetic series of phone calls with Western allies, as well as to Mr Putin and Ukrainian leader Volodymyr Zelenskyy.

On Sunday, a French presidency source said Mr Macron had spoken with Mr Biden on a 40-minute-long call ahead of his trip to Moscow in a "coordination logic".

The conversation is said to have allowed the two leaders to "share information about contacts made during the weekend" for good coordination ahead of the trip, the source said.

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"We're heading to Putin's lair, in many ways it's a throw of the dice," one source close to Mr Macron reportedly told Reuters news agency.

Russia has placed more than 100,000 troops near its border with Ukraine, but Mr Putin has denied he is planning an attack.

Read more: Politician accused in alleged plot to install 'pro-Kremlin' leader wants apology from UK

It has demanded NATO and US security guarantees, including that NATO never admits Ukraine as a member.

Meanwhile, the UK Labour Party called on the government to halt a plan to cut the British Army by another 10,000 troops, given the ongoing crisis.