Blair said he spoke on Monday morning with Anders Fogh Rasmussen, the prime minister of Denmark, where the cartoons were first published, to offer Britain's full support and say that they stand together in solidarity.
Blair also condemned the aggressive tone of protesters in London.
In a statement, Blair said: "The attacks on the citizens of Denmark and people of the European community were completely unacceptable, as is the behaviour of some of the demonstrators in London over the past few days."
"The police shall have our full support in respect of any action they wish to take with respect to upholding the law, though we understand the difficult situation they were facing."
Protesters have destroyed Danish embassies in Syria and Lebanon, and rioted in Afghanistan on Monday.
During peaceful protests in London against the cartoons on Friday and Saturday, some of the demonstrators carried signs urging "the beheading of infidels" and warning that a 9/11 type attack is on its way in Europe.
Blair's spokesman said it was for the police and Britain's Crown Prosecution Service to decide whether arrests or prosecutions were justified regarding the London protesters.
"The attacks on the citizens of Denmark and people of the European community were completely unacceptable, as is the behavior of some of the demonstrators in London over the past few days"
UK Prime Minister
The spokesman also welcomed statements by Muslim leaders in Britain condemning London protesters who carried posters threatening violence against those who published the cartoons.
Inayat Bunglawala, a spokesman for the Muslim Council of Britain, said on Sunday that the Muslim community would welcome eventual arrests and prosecutions of those brandishing "disgraceful" placards at Friday's demonstration in London.
Bunglawala said on Channel 4 news: "I think the police were right to have taken footage of the event and identified the ring leaders, because although several hundred people were there, the actual placards were being held by a tiny group of extremists."