Biden said on Tuesday personal sanctions on Putin, though a rare step, could be considered as part of a concerted drive by the United States and its allies to convince Moscow that any new aggression against Ukraine would bring swift and massive costs.
Kremlin spokesman Dmitry Peskov on Wednesday said US Congressmen and senators discussing personal sanctions against Russia's top leaders were ignorant of the fact they were legally barred from holding assets, property and bank accounts abroad.
Individual sanctions against Putin would be "not painful (but) politically destructive", said Peskov, who has previously said they would amount to severing diplomatic relations.
As officials began four-nation talks in Paris, Russia held new military drills on land and sea and moved more paratroops and fighter jets to Belarus, north of Ukraine, for what it describes as joint exercises there next month.
Ukraine said Russia, which has gathered tens of thousands of troops near its border but denied plans to invade, was trying to sow panic. Foreign Minister Dmytro Kuleba said Moscow had not yet massed sufficient forces for a large-scale offensive, but that did not mean it could not do so later.
Nearly eight years after Russia seized Crimea and backed separatist fighters in Donbass in eastern Ukraine, the former Soviet republic has become the flashpoint in potentially the most dangerous East-West confrontation since the Cold War.
Russia says the crisis is being driven by NATO and US actions, and is demanding security guarantees from the West, including a promise by NATO never to admit Ukraine. Moscow sees Ukraine as a buffer between Russia and NATO countries.
Western allies have threatened economic sanctions against Russia if it attacks Ukraine, and the United States has been talking to major energy-producing countries and companies around the world over a potential diversion of supplies to Europe if Russia invades Ukraine.
The EU depends on Russia for about a third of its gas supplies. Any interruptions to its Russian imports would exacerbate an existing energy crisis caused by shortages.
In Paris, officials from France, Germany, Russia and Ukraine began talks on the simmering Donbass war in which some 15,000 people have been killed since 2014.
Andriy Yermak, chief of staff to Ukraine's President Volodymyr Zelenskiy, called the talks "a strong signal towards achieving peace in eastern Ukraine".
But he said major ceasefire violations were taking place, and ruled out the prospect of speaking directly to the separatists.
The four-way "Normandy format" talks, which have not been held for more than six months, are seen by the European powers as vital to remaining relevant in the broader dialogue with Moscow while the United States and NATO hold separate crisis negotiations.
A French presidential official said the aim was to set a date for talks on humanitarian measures and prisoner releases that would then lead to negotiations on the future of the Donbass region. However, he said the reality was that they would use the Paris talks to determine whether Russia was serious.
Interfax news agency quoted the Russian defence ministry as saying it a paratrooper unit had been deployed to Belarus on Wednesday, a day after moving in artillery forces and marines ahead of joint exercises next month.
It said Russia was also moving Su-35 fighter jets to Belarus for the "Allied Resolve" exercises.
The build-up of Russian forces in Belarus, a close Russian ally and former Soviet republic north of Ukraine, creates a new front for a possible attack.
RIA news agency said more than 20 Russian vessels had embarked on exercises in the Black Sea, south of Ukraine.
Separately, Russian artillery forces in the southern Rostov region that borders Ukraine were set to practise firing on Wednesday as part of a combat readiness inspection of the Southern Military District, the defence ministry said.
