The protesters said they were reclaiming 5 Belgrave Square, in central London, for Ukrainian refugees.
Billionaire energy tycoon Mr Deripaska is one of the oligarchs sanctioned by the UK government following Russia’s invasion of Ukraine.
Riot police entered the property earlier but found nobody inside.
The Metropolitan Police said it was “continuing to engage with those on the balcony as we balance the need for enforcement with the safety of all involved”.
The group is named the London Makhnovists, after the Ukrainian anarchist Nestor Makhno, who revolted against the Russian White Army in 1918-21.
Standing on the balcony, one of the protesters told journalists they were doing the government’s work for them by reclaiming the building for refugees fleeing their homes.
He said: “[Home secretary] Priti Patel, don’t worry, we did your job – we did the housing, just send them here, we did the housing. Refugees welcome!
“We’re demanding this property belong to Ukrainian refugees. Their houses have been destroyed and this guy [Deripaska] supported the war.
“He knew the war was coming but he said nothing. His silence is violence.”
The protesters said there were about 200 rooms in the “ridiculous” mansion, which was “filthy fancy” and had “so much stuff a normal human being would never need”, including a home cinema and works of art.
Another added: “[Michael Gove] said oligarchs’ homes should be expropriated to house Ukrainian refugees.
“We’re doing the government’s work for them and we’re doing it for free, so I expect a significant rebate on my tax bill later on in April.”
The Met Police were called to the scene at 01:00 GMT, when a spokesperson said reports a number of people had “gained entry” to the “large and complex” property.
Eight police vans pulled up outside the mansion at about noon and riot officers started attempting to gain entry.
A ladder put up against the balcony was pushed back by the protesters and officers then started drilling through the front door.
A police spokesperson said they had searched the mansion, and were “satisfied” that no protesters were inside, although four men are still sitting on the edge of a balcony, and officers are “considering the appropriate next steps”.
Speaking about the possibility of arrest, one said “all our group made peace with arrest because this was always one of the options. I’m ready to take the consequences for something I believe”.
One account supporting the protesters online, Resist London, said the group was protected by “the protest defence” because they had no intention of living and sleeping there.
In response, the prime minister’s official spokesman said: “Squatting in residential buildings is illegal.
“But we are working to identify the appropriate use for seized properties while owners are subject to sanctions.”
He also confirmed Downing Street was examining whether the properties of sanctioned oligarchs could be used to house Ukrainian refugees, although it is thought new legislation would be required.
“Certainly that’s something we are looking at,” he said. “I think in the first instance the two (visa) routes that we have are how we expect people will be housed in the UK, either through family or through this sponsorship route.”
Ivan, who was passing by, said he is originally from Lviv in western Ukraine and was fully in support of the protest.
“I think it’s very good,” he said, adding he believed the mansion belonged to Mr Deripaska, who is “a friend of Putin”.
“My people are suffering and they need help,” he said.
Other passers-by were supportive of the occupation, saying they were unable to protest themselves but the action would make a difference.
One man said: “We need to protest in every way we can because this war is not right. A lot of civilians and women and children are dying every day for Putin and it’s unbelievable.”
Charles Delingpole, who said he works in the field of sanctions, said he supported the protest but it was important to uphold the rule of law.
He said: “I think the UK has been too slow to sanction Russian oligarchs based on an abundance of caution as opposed to due process.
“However, this is the breakdown of law and just because we fight with monsters doesn’t mean we need to turn into them ourselves.”
Mr Deripaska, founder of metals and hydropower company EN+, has been under US sanctions since 2018 as a result of his alleged close relationship with the Kremlin.
A 2006 High Court judgement revealed Mr Deripaska was the beneficial owner of Five Belgrave Square.
The seven-bedroom house, in one of London’s most expensive neighbourhoods, also has a home cinema, a gym and a Turkish steam bath.
The property had been bought through Ravellot Limited, an offshore company incorporated in the British Virgin Islands, and the business still owns the property.
Land Registry documents give Graham Bonham Carter as the contact for Ravellot.
Five bank accounts held by him are subject to asset freezing orders at the request of the National Crime Agency (NCA), following the Russian invasion of Ukraine.
The bank accounts were frozen because of suspected links to Mr Deripaska, the NCA said.
