Cheney rejects gay marriage ban - BBC
Mr Cheney was addressing a campaign audience in Iowa that included his daughter, Mary, who is openly lesbian.
He said the issue of legalising gay unions should be settled by individual states rather than by Washington.
However, Mr Cheney said he accepted the views of Mr Bush, whose opposition to gay marriage is well publicised.
President Bush recently backed a motion calling for a federal ban on gay marriage, prompted by attempts in some US states to have same-sex unions legalised.
The motion was defeated when Republican senators sided with Democrats on the issue.
Vice-President Cheney said he and his wife "have a gay daughter, so it's an issue our family is very familiar with".
Regarding the issue of same-sex relationships, he said, "my general view is freedom means freedom for everyone".
He said individual states have historically decided "what constitutes a marriage".
Mr Cheney has said his views are personal and have no bearing on White House policy.
However, says the BBC's Dan Griffiths in Washington, they strike at the very heart of President Bush's thinking and should revive debate around the issue just days before the Republican convention in New York.
While gay rights activists welcomed Mr Cheney's comments, there was criticism from some conservatives.
Genevieve Wood of the Family Research Council said Mr Cheney's remarks were disappointing and sent out "a mixed message to voters".
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