Speaking on an ABC News interview on Tuesday, the president said people should be able to make all "arrangements" they want as long as a state recognizes them.
A steadfast opponent of gay marriage, Bush now appears to support a constitutional amendment to laws that enshrine heterosexual marriage.
"If necessary, I will support a constitutional amendment... whatever legal arrangements people want to make, they're allowed to make, so long as it's embraced by the state or at the state level."
Heading into his re-election campaign, the president is walking a fine line between the interests of his social conservative base - which favours a constitutional ban on gay marriage - and other voters who have shown more acceptance of same-sex unions.
The issue emerged last month when a Massachusetts court ruled in favour of it, prompting calls from some conservatives for a constitutional amendment to say marriage could only be between a man and a woman.
"The court I thought overreached," Bush said. "It did the job of the legislature. It was a very activist court in making the decision it made."
The Massachusetts ruling was preceded by a US Supreme Court decision in June which struck down a Texas sodomy law.
The move raised speculation that laws barring gay marriage may be vulnerable to challenge nationally unless the constitution was amended.
However, Bush continues to support federal legislation that defines marriage as heterosexual and allows states to refuse to recognize any same-sex marriage performed elsewhere, according to the White House spokesman.
White House says Bush remarks
do not mean a change in policy
The president's comments, however, have appeared to upset both supporters and detractors of a change in legislation.
"This sounds as though the administration would support civil unions which are counterfeits of the institution of marriage," said Tony Perkins, president of the Family Research Council.
But political director Winnie Stachelberg of the Human Rights campaign, a gay and lesbian rights group, said "it's never necessary to amend the constitution in this way."
She said an anti-gay marriage constitutional amendment now before Congress could strip existing state protections of gay and lesbian relationships.
Polls and statistics
Spokesman Mark Mead of the Log Cabin Republicans, representing gay and lesbian party members, said the group was pleased with Bush's states'-rights position. "Leaving it up to the states is what conservative Republicans should support."
A Pew Research Centre poll taken in October showed that 59% of Americans opposed gay marriage, but 51% favoured giving same-sex couples some of the same legal rights of marriage.
It said only 10% preferred amending the constitution to ban gay marriage, but 42% supported prohibiting gay marriage by law.
Amending the constitution requires a two-thirds vote by each house of Congress and ratification of three-fourths of states. Since the adoption of the original 10 amendments in the Bill of Rights, there have been 17 amendments.