Cabinet minister Nadhim Zahawi said whether to overthrow Mr Putin for his invasion of Ukraine is "up to the Russian people" after the US President's unscripted call caused the White House to insist that it had no plans for regime change in Moscow.
Meanwhile Ukrainian president Volodymyr Zelensky accused the West of lacking courage in helping his country fight Russia's invasion, making a plea for fighter aircraft and tanks. He criticised the West's "ping-pong about who and how should hand over jets and other defensive weapons to us" while Russian missile attacks kill and trap civilians.
In his speech in Warsaw, Mr Biden appealed to Russian people directly with comparisons between the invasion of Ukraine and the horrors of the Second World War.
"For God's sake this man cannot remain in power," he said at the close of his speech about the Russian president he had earlier described as a "butcher".
As multiple rockets struck the city of Lviv near the Polish border in the west of Ukraine, Mr Biden pleaded: "If you're able to listen – you, the Russian people, are not our enemy."
But a White House official argued that the US president's point was that the Russian leader "cannot be allowed to exercise power over his neighbours or the region".
US secretary of state Antony Blinken insisted "we do not have a strategy of regime change" as the Kremlin said it is "not up to the Americans to decide who will remain in power in Russia".
Richard Haass, a veteran US diplomat who is president of the Council on Foreign Relations think-tank, said Mr Biden's remarks made "a dangerous situation more dangerous" when the strategy should be focused on de-escalation.
UK Education Secretary Mr Zahawi said it is "for the Russian people to decide how they are governed" but suggested they "would certainly do well" to have someone who "is democratic and understands their wishes.
"That's up to the Russian people and it is only the Russian people that can make that decision, I suspect most of them are pretty fed-up with Putin and his cronies and the illegal war," he told the BBC's Sunday Morning show.
But he declined to criticise Mr Biden, unlike Tobias Ellwood, the Conservative MP who chairs the Commons defence committee, who said Mr Putin will now "spin this, dig in and fight harder".
Asked if Mr Biden was wrong to issue the call, Mr Zahawi told Sky's Sophy Ridge on Sunday: "No, what I'm saying to you is the White House has been very clear on this, the president gave a very powerful speech on this and I think both the United States and the United Kingdom agree that it's up to the Russian people to decide who should be governing them."
He backed his Cabinet colleague Liz Truss in saying sanctions on oligarchs, banks and businesses could be lifted if Mr Putin ends the war and commits to "no further aggression".
With the Kremlin's troops struggling, the Foreign Secretary's comments will be seen as a possible incentive for Mr Putin to cut his losses and reach a deal with Ukraine.
She said: "Those sanctions should only come off with a full ceasefire and withdrawal, but also commitments that there will be no further aggression.
"And also, there's the opportunity to have snapback sanctions if there is further aggression in future. That is a real lever that I think can be used."
Moscow has indicated it could scale back its offensive to focus on what it claimed was the "main goal, liberation of Donbas", the region bordering Russia in the east of Ukraine. But Mr Zelensky warned he would not give up territory in peace talks as he noted that his troops have delivered "powerful blows" to invading forces.
Asked if Moscow was changing strategy to focus on Donbas, Mr Zahawi said the Russian military is having "real problems" on the ground as the Ukrainians have "fought like lions".
The latest update from the Ministry of Defence said the Kremlin's forces "appear to be concentrating their effort to attempt the encirclement of Ukrainian forces" in the east.
"The battlefield across northern Ukraine remains largely static with local Ukrainian counterattacks hampering Russian attempts to reorganise their forces," it added.
In a video address yesterday, Mr Zelensky referred to the besieged southern city of Mariupol. He said: "I've talked to the defenders of Mariupol today. I'm in constant contact with them. Their determination, heroism and firmness are astonishing.
"If only those who have been thinking for 31 days on how to hand over dozens of jets and tanks had 1 per cent of their courage."
Russia's invasion, now in its 33nd day, has stalled in many areas, faltering in the face of Ukrainian resistance bolstered by weapons from the West.
Military aid has not included fighter jets. A proposal to transfer Polish planes to Ukraine via the US was scrapped amid Nato concerns about getting drawn into conflict with Russia.
"So who is in charge of the Euro-Atlantic community? Is it still Moscow, thanks to its scare tactics?" Mr Zelensky said. "Our partners must step up their aid to Ukraine."
Russia’s defence ministry said that it used air-launched cruise missiles to hit a fuel depot and a defence plant in Lviv.
It said another strike with sea-launched missiles destroyed a depot with air defence missiles in Plesetske, just west of Ukraine's capital Kyiv.
Early yesterday, a chemical smell still lingered in the air as firefighters in Lviv, about 45 miles from the Polish border, sprayed water on a burned section of an oil plant hit in the Russian attack.
Russia's air strikes shook the city that has become a haven for an estimated 200,000 people who have fled bombarded towns and cities.
Lviv also has been a stopping point for most of the 3.8 million refugees who have fled Ukraine since Russia invaded.
Missiles struck an aircraft repair factory near the main airport there a week ago.