Russia's military said on Monday Ukrainian military saboteurs had tried to enter Russian territory in armed vehicles, an accusation dismissed as "fake news" by Kyiv amid Western accusations that Moscow could fabricate a pretext to invade.
The Russian military said five people had been killed when the Ukrainian saboteurs were thwarted.
Ukraine and its Western allies have been saying for days that Moscow could manufacture a pretext to invade Ukraine with a huge force it has massed on the border, reports Reuters.
Western countries accuse Russia of planning to invade a neighbour that it had controlled until the Soviet Union collapsed in 1991. Moscow denies planning any attack but has demanded sweeping security guarantees, including a promise that Ukraine will never join NATO.
Hours earlier, French President Emmanuel Macron said Russian President Vladimir Putin and his US counterpart Joe Biden had agreed in principle on a meeting.
An adviser to French President Emmanuel Macron told Reuters that Macron had put the proposal to Putin at Biden's request.
Kremlin spokesperson Dmitry Peskov said a call or meeting between Putin and Biden could be set up at any time, but there were no concrete plans yet for a summit. Tensions were growing, he said, but a foreign ministers' meeting was possible this week.
Macron's office and the White House said the substance of the plan would be worked out by US Secretary of State Antony Blinken and Russian Foreign Minister Sergei Lavrov during a meeting planned for Thursday.
European financial markets were tumbling on Monday at signs of increased confrontation, after having briefly edged higher on the glimmer of hope that a summit might offer a path out of Europe's biggest military crisis in decades.
After the report of the alleged incursion, major European bourses were down between 0.5 per cent and 1.8 per cent. Russian stocks plunged.
Russia's military said troops and border guards had prevented a "diversionary reconnaissance" group from breaching Russia's border from Ukrainian territory near Rostov and that five people had been killed, Russian news agencies reported.
Interfax cited the Russian military as saying that Ukrainian armed vehicles had been destroyed.
Ukraine rejected the report, calling it fake news, and said no Ukrainian forces were present in the Rostov region where the incident was alleged to have taken place.
Satellite imagery released at the weekend appeared to show Russian deployments closer to Ukraine's border than before.
Nerves frayed further when Moscow's close ally Belarus announced on Sunday that Russia would extend military exercises there.
Russia has tens of thousands of soldiers in Belarus - part of what Washington says is a force now numbering 169,000-190,000 troops in the region, including pro-Russian rebels in eastern Ukraine.
After talks in Brussels with NATO Secretary-General Jens Stoltenberg, British foreign minister Liz Truss said Western countries were preparing for a "worst-case scenario". The airlines Lufthansa, KLM and Air France all cancelled flights to Kyiv.
But the European Union rebuffed a call from Kyiv to impose some sanctions now to try to avert war before it started.
