Prime Minister Tony Blair has told the BBC Jack Straw's decision to open a debate about Muslim women wearing full face veils was "perfectly sensible".
Gordon Brown has backed Commons leader Jack Straw over his comments on Muslim women wearing veils.
Mr Straw suggested wearing full face veils could harm community relations.
The chancellor told BBC's political editor, Nick Robinson, it was important to "have a proper debate".
Mr Blair said the Commons leader had raised the issue in a "measured and considered" way, and cautioned against people getting "hysterical" about it.
Last week, Mr Straw said it would be better for integration if women did not wear veils as they were "a visible statement of separation".
Author Salman Rushdie backed Mr Straw, saying that veils "suck" as they were a symbol of the "limitation of women".
Earlier, Prime Minister Tony Blair said his colleague had been "perfectly sensible" in raising the issue.
'Break down barriers'
'Cultural changes'
The subject arose after Mr Straw said last week that he now asked Muslim women to take off full veils at his constituency surgery.
Asked on BBC One's Six o' Clock News whether Mr Straw had been right to say it would be better for integration if people did not wear veils, Mr Brown said: "Yes, but I think he's not proposing new laws.
Mr Blair said it was important to raise such issues "if we want to break down barriers" between people, cultures and religions.
"He's proposing a debate about the cultural changes that might have to take place in Britain, and I would emphasise the importance of what we do to integrate people into our country, including the language, including history, including the curriculum."
He stopped short of saying he would make the same request as Mr Straw, but said having a debate was important.
Then asked if he thought it would be "better for Britain" if fewer people wore veils, Mr Brown replied: "Well that's what Jack Straw has said and I support."
"I think it's perfectly sensible if you raise it in a measured and considered way which he did, to have a proper public discussion about it," Mr Blair said.
The integration debate had to look at citizenship ceremonies and the teaching of British history, he said.
"How do we make sure people integrate more, how do we make sure people aren't wanting to separate themselves out from the mainstream of society?"
Mr Brown also said immigrants "should speak the language of English".
Chancellor Gordon Brown told the BBC he supported Mr Straw for opening up a debate on veils.
'Measured, considered'
But he added that discussions should be about Britishness - teaching the English language, citizenship and British history.
Earlier, Mr Blair said the Commons leader had raised the issue in a "measured and considered" way, and cautioned against people getting "hysterical" about it.
It was time to "extinguish the heat that ignites the extremists' fire", Mr Brown said.
Author Salman Rushdie also backed Mr Straw, saying that veils "suck" as they were a symbol of the "limitation of women".
Mr Straw said last week he did not want to be "prescriptive" but he believed that covering people's faces could make community relations more difficult.
The controversy arose after Mr Straw said last week that he now asked Muslim women to take off full veils at his constituency surgery.
He is Labour MP for Blackburn, where between 25% and 30% of residents are Muslim.
He said he did not want to be "prescriptive" but he believed that covering people's faces could make community relations more difficult.
"Communities are bound together partly by informal chance relations between strangers - people being able to acknowledge each other in the street or being able to pass the time of day," he said.
Mr Straw is Labour MP for Blackburn, where between 25% and 30% of residents are Muslim.
"That's made more difficult if people are wearing a veil. That's just a fact of life."
Some Muslims have called his remarks insulting but others said they understood his concerns.
Some Muslims called his remarks insulting but others said they understood his concerns.
Mr Rushdie, who was once the subject of a fatwa by Ayatollah Khomeni of Iran over his novel The Satanic Verses, told BBC Radio 4's Today programme he saw veils as removing power from women.
Mr Straw "was expressing an important opinion which is that veils suck - which they do," the author added.
"Speaking as somebody with three sisters and a very largely female Muslim family, there is not a single woman I know in my family or in their friends who would have accepted the wearing of a veil.
"The battle against the veil has been a long and continuing battle against the limitation of women so, in that sense, I am completely on his side."
