Marriage is "a celebration of love and should be open to everyone", Equalities Minister Lynne Featherstone said as she published plans to legalise gay civil marriage.
She signalled the Government's determination to make the change by 2015, at an expected cost of £4 million, putting ministers on collision course with church leaders and many Conservatives.
Tory MPs are expected to be offered a free vote when legislation championed by Prime Minister David Cameron comes before the Commons in a bid to prevent an embarrassing backbench revolt.
Under the plans put out for consultation today, same-sex couples will be entitled to get married in a register office or other civil ceremonies, or convert existing civil partnerships.
Existing marriages in which one partner changed their sex would also no longer have to be ended.
The blueprint however, also endorsed by home Secretary Theresa May, maintains a legal ban on same-sex religious services despite some churches expressing an interest in conducting them.
Nor does it anticipate allowing heterosexual couples to enter civil partnerships, the state-recognised partnerships introduced in 2005 as a first step towards gay marriage.
In a joint foreword, the two ministers said the present discrimination was unacceptable.
“Put simply, it's not right that a couple who love each other and want to formalise a commitment to each other should be denied the right to marry,” they wrote.
The reforms have sparked a wave of religious fury, with Britain's most senior Catholic branding the proposal a “grotesque subversion of a universally acknowledged human right”.
Many Tory MPs are also known to be hostile to the change which is seen as an example of Liberal Democrat influence on coalition policy despite Mr Cameron's public support.
Half the party's grassroots supporters are against the change, a recent poll suggested, though it was backed by a margin of 45% to 36% among the wider public.
The Prime Minister championed reform in his party conference speech, declaring: “I don't support gay marriage despite being a Conservative. I support gay marriage because I'm a Conservative.”
But it is understood party whips are set to ensure the issue is treated as a matter of conscience when it is ready to be debated by Parliament amid fears of a major revolt.
A Downing Street spokeswoman refused to be drawn on whether MPs would be expected to back the Government but noted that Mr Cameron has made his views “very clear”.
She said: “Any vote is some time away so I'm not aware of any whipping arrangements. We have just published a consultation today. We are not there yet in terms of the process.”
She added: “The Prime Minister's views are very clear. He's fully in support of it.”
Setting out the proposed changes, Ms Featherstone said: “Today is a hugely important step as we consider how to lift the ban on civil marriage for same-sex couples. This is about the underlying principles of family, society and personal freedoms. Marriage is a celebration of love and should be open to everyone.”
She made clear there was no question of the principle being reopened, however strong the opposition to gay marriage became.
One campaign group, The Coalition for Marriage, has placed adverts in two national newspapers to coincide with the launch of the consultation, which call the proposals “profoundly undemocratic”.
Labour welcomed the proposals, calling for legislation to be included in May's Queen's Speech, but said the Government should allow churches to marry gay couples if they chose to.
Shadow home secretary Yvette Cooper said: “No one is proposing that churches should be obliged to hold same-sex marriages. That is rightly ruled out in this consultation. Religious marriages are a matter for each church and denomination, not for the Government. But equally, the Government should go further than they currently plan.
“If we really support the institution of marriage and want to welcome more people into it, then government and parliament should not deny the Quakers, the Unitarians and other churches who want to celebrate gay marriage the chance to do so.”
Peter Tatchell, co-ordinator of the Equal Love campaign, called for civil partnerships to be extended to heterosexual couples, suggesting not to do so breached human rights.
The changes, which would affect England and Wales, were backed by the Family and Parenting Institute charity.
Chief executive Katherine Rake said: “As a society we need to do all that we can to support stable couple relationships. Stability is vital for the well-being of children. The wider members of a family around the couple also benefit.
“It's important for UK society to offer all couples a genuine choice on how they can best achieve this stability. Gay couples should be allowed to choose civil marriage if they decide it's the best option for them.”
But the consultation was dubbed a “sham” by the Coalition for Marriage (C4M), which counts several Tory and Labour MPs and a number of Church of England bishops among more than 200,000 signatories to an online petition.
Campaign director Colin Hart said: “This consultation is a sham. It is being pushed through despite the public never having a say on this change. None of the main political parties proposed redefining marriage in their manifestos and the impact assessment misses out many of the possible problems that could occur if this institution is redefined. For example, how this change will affect our schools.
“C4M and the 200,000 people who have signed our petition believe that this change is profoundly undemocratic, will have massive consequences for society and is simply unnecessary as civil partnerships provide all the legal rights of marriage.”
UK Independence Party spokesman David Coburn said: “It seems that through some kind of political correctness, David Cameron is picking a fight with the millions of people whose religious faiths do not recognise same-sex marriages.
“That, in our view, is an aggressive attack on people of faith and an act of intolerance in itself. This is a concern that must be expressed in the consultation.”
The impact assessment published alongside the consultation puts the cost of the change, mainly in terms of changing IT systems and staff training, at up to £4.5 million.
It noted that after an initial flurry, the number of civil partnerships being entered has steadied at around 58,000 per year, with between 68,000 and 88,000 now in place.
One advantage of the new system would be allowing same-sex couples to keep their sexuality hidden. At present, being in a civil partnership automatically signifies a couple is gay.
Wedding venues such as hotels would be able to carry out same-sex civil ceremonies under their existing licences, the assessment suggested.
One Tory MP opposed to the change suggested it would open the door to other claims, such as legalising Islamic marriages involving multiple wives.
Julian Brazier, who opposed the introduction of civil partnerships, said he did not have a problem "with people forming these relationships".
But he told BBC Radio 4's The World At One: "If we are going to say to the gay lobby that we are going to revise, completely change, this definition from one man and one women, what do we then say to the much larger group of Islamic people in this country?
"They have, in sharia marriage, up to four wives. Why are we making a change for one group but refusing it to a larger group?"
Advocates of civil partnerships had insisted at the time that they were not a first step to same-sex marriage, he pointed out.
"It, of course, within seven years has turned into exactly that.
"I do not have a problem with people forming these relationships. I do not have a problem with changes in the law to reflect the international problems.
"But it seems to me that the institution of marriage, which has been with us for more than 2,000 years, is fundamental."
Tory MPs had "a free vote and a variety of different views", he said, denying the issue was a clash between the two sides of the coalition.
Tory MP Peter Bone said he "threw up" when the Prime Minister told his party he supported gay marriage "because" he was a Conservative.
He told Ian Payne on LBC 97.3: "I threw up when I heard that comment. It was at the party conference and on what authority he had to say that, I do not know and that's why, if you listen to what he said, he's making that a party political thing.
"It's saying you have to vote for gay marriage because you're a Conservative. There is absolutely no basis whatsoever for saying that.
"He can, of course, support gay marriage if that's what he believes in, but he can't pretend this is Conservative policy, tradition or anything.
"The Prime Minister is doing a lot of good things for the country but on this particular issue, he is totally and utterly wrong."