David Cameron and Nick Clegg have been asked to legalise full gay marriage
Mr Tatchell, says banning gay couples from having civil marriages was the "last homophobic law in the UK".
During the election campaign, a Tory equality manifesto drawn up by Theresa May said the party would "consider the case" for allowing civil partnerships to be called marriage.
However, Mr Cameron then said he was "not planning" to make any changes.
Liberal Democrat leader and new deputy prime minister Nick Clegg said earlier this year he supported full marriage equality but his party's LGBT manifesto did not contain any promise on the issue.
Writing for the Independent, Mr Tatchell argued that the issue was "an elephant in the room" and said a poll last summer showed 61 per cent of the public agreed gay couples should be able to have civil marriages.
He said civil partnerships had created a "two-tier system of relationship recognition and rights".
He added: "Imagine the outcry if the government reserved marriage for white people and introduced a separate partnership register for black couples. It would provoke accusations of racism and apartheid – and international condemnation.
"If the government is sincere in its commitment to gay equality, it should forget about fancy Downing Street receptions and concentrate on delivering gay rights policies, including marriage equality."
The Civil Partnerships Act 2004 gave gay couples all the rights and benefits available to straight married couples.
There are two differences between the ceremonies. One is that a civil partnership is formed when the second of the two parties signs the partnership papers, while a marriage happens when the partners exchange spoken words and sign the register.
The other is that civil partnerships cannot be carried out by a religious minister or held in a church. Straight couples cannot have a civil partnership.
Stonewall says civil partnerships are adequate, although it has lobbied in the last year for the law to be changed to allow them to be held in churches.
Mr Tatchell, says the difference is not acceptable.
Seven European countries – including Spain and Iceland – now allow gay couples access to full civil marriage.
