The Kremlin confirmed that Anatoly Chubais had resigned of his own accord, the first senior official to break with the government since Putin launched his invasion a month ago.
Chubais was one of the principal architects of Boris Yeltsin's economic reforms of the 1990s and was Putin's boss in the future president's first Kremlin job.
He held senior business and political jobs under Putin, lately serving as Kremlin special envoy to international organisations.
Chubais hung up the phone when contacted by Reuters.
The sources did not say where he was.
Many Russians blame Chubais for allowing a small group of tycoons to enrich themselves in the privatisations of the 1990s while millions of Russians were left in poverty amid economic collapse and crisis.
In recent years he continued to call for economic reform and was one of the most high-profile liberals associated with the Russian government.
Biden flies to Europe on Wednesday for an emergency NATO summit on Ukraine where invading Russian troops are stalled, cities are under bombardment and the besieged port of Mariupol is in flames.
Four weeks into a war that has driven a quarter of Ukraine's 44 million people from their homes, Russia has failed to capture a single major Ukrainian city, while sanctions have ostracised it from the world economy.
Russia says its aim is to disarm its neighbour, and its "special military operation" is going to plan.
It denies targeting civilians.
Worst hit has been Mariupol, a southern port completely surrounded by Russian forces, where hundreds of thousands of people have been sheltering since the war's early days, under constant bombardment and with food, water and heat supplies cut.
New satellite photographs from commercial firm Maxar showed massive destruction of what was once a city of 400,000 people, with columns of smoke rising from residential apartment buildings in flames.
No journalists have been able to report from inside the Ukrainian-held parts of the city for more than a week, during which time Ukrainian officials say Russia has bombed a theatre and an art school used as bomb shelters, burying hundreds of people alive.
Russia denies targeting those buildings.
Biden, due to arrive in Brussels on Wednesday evening on his first foreign trip since the war began, will meet NATO and European leaders in an emergency summit at the military alliance's headquarters.
The leaders are expected to roll out additional sanctions against Russia on Thursday.
Sources said the US package would include measures targeting Russian members of parliament.
Biden will also visit Poland, which has taken in most of the more than 3.6 million refugees who have fled Ukraine and has been the main route for foreign supplies of weapons to Ukraine.
Poland announced it was expelling 45 Russian diplomats accused of either being undercover spies or "associated" with them.
Several other eastern European countries have announced similar moves in recent days, although not on such a large scale.
Russia has rejected all the accusations.
For Ukrainians, life continues under the relentless bombardment.
In Kharkiv in the east, a maternity clinic had moved patients into the basement for safety.
Tearful mother Yana cradled her baby in a room with beds lining the walls.
Her house has been bombed.
"I have nowhere to go," she said.
Far away in Mykolaiv, a southern port which Russian forces tried and failed to storm over the past 10 days, Tamara Kravchuk, 37, lay blissfully with her baby just minutes old on her chest.
She had been scared, especially when explosions burst just 500 metres from the hospital, she said.
But baby Katya melted her fears away.
"I think the war will end and we will live as it was before, our life will be calm again," she said.
"I hope our children won't see all these crazy things and everything will be good."