The prime minister held back from calling for the football tournament to be taken away from Russia after Nick Clegg, the deputy prime minister, said it was "unthinkable" that the contest could be held there if the country's belligerence continues.
Labour's shadow foreign secretary, Douglas Alexander, urged football's governing body, Fifa, to draw up contingency plans for the event to be held elsewhere.
Some German politicians have already called for the 2018 World Cup bidding contest to be re-run after international condemnation of Russia over its reaction to the crash of Malaysia Airlines flight MH17 in Ukraine.
The Kremlin denies that any of its weapons were used to shoot down the plane but the UK, US and Ukraine have all said there are strong reasons to suspect the plane was shot down accidentally by pro-Putin separatists using a Soviet-era missile supplied by Russia.
Number 10 would not join those suggesting the football event should be cancelled, but the fact that this is being mooted by some "shows the importance of Russia changing course, before its international standing is damaged even further", a spokesman said.
"The prime minister does not believe we should reach immediately for boycotts, but it is also not surprising, given Russian behaviour, that people are starting to raise the issue."
Fifa has ruled out a boycott, insisting the tournament could be "a force for good". However, Clegg told the Sunday Times that stripping Russia of major sporting events would be a "very potent political and symbolic sanction".
"Vladimir Putin himself has to understand that he can't have his cake and eat it," the Liberal Democrat leader said. "He can't constantly push the patience of the international community beyond breaking point, destabilise a neighbouring country, protect these armed separatists in the east of Ukraine and still have the privilege and honour of receiving all the accolades in 2018 for being the host nation of the World Cup.
"That's why I've come to the view that if he doesn't change course it's just not on, the idea that Russia will host the World Cup in 2018. You can't have this – the beautiful game marred by the ugly aggression of Russia on the Russian-Ukrainian border.
"Not only would Vladimir Putin exploit it, I think it would make the rest of the world look so weak and so insincere about our protestations about Vladimir Putin's behaviour if we're not prepared to pull the plug."
Clegg also raised "question marks" over Russia holding the Grand Prix in Sochi in October. "Vladimir Putin is a past master at attending these sporting events and, sort of, pretending almost as if everything's utterly normal and nothing untoward is happening around him," he said.
"And if anyone needed any reminding of how dangerous this conflict is in the heart of Europe, just ask any of the family and relatives of those loved ones they lost in that plane incident last week."
Clegg has also joined Cameron's criticism of a French deal to supply warships to Russia, saying it would be "wholly inappropriate" for it to proceed in the present circumstances.
"Whilst I can entirely understand that the French may have entered into that contract with the Russians in entirely different circumstances, it is wholly inappropriate to go ahead with that now," he said.
"And as you know, the prime minister has reviewed the outstanding licenses that we have got to make sure that we deliver what we unilaterally announced back in March, which was that there would be no exports from Britain of arms products which could in any way fuel or fan the flames of the conflict in Ukraine."
Labour's Alexander said Fifa needed to think about who else could hold the World Cup in 2018 if it is proven that Russia had responsibility for the Malaysian airliner crash.
"If it is confirmed that Russia carries direct responsibly for downing flight MH17, and the Kremlin nonetheless continues to sponsor and fuel the conflict in Ukraine, then Fifa will surely face calls to reconsider if Russia should host the competition in 2018," he said. "Fifa should therefore be undertaking contingency planning now so that, if required, alternative plans are in place in plenty of time for teams and fans from around the world.
"The Ukraine crisis represents not just a threat to European security, but a significant geopolitical moment, and together, Europe must work harder to better influence critical calculations now being made in the Kremlin."
guardian.co.uk © Guardian News and Media Limited 2010