Mr Twigg (right), who is one of three openly gay Labour members, alongside Ben Bradshaw, the Exeter MP and Chris Smith, the Secretary of State for National Heritage, helped to launch a new drive for equal rights.
It was the responsibility of MPs of all parties to back the case for homosexual equality before the law, he said.
"This is an issue of human rights, to be taken up by all MPs, not just those of us who are gay. This is one of those issues on which Parliament should seek to lead public opinion."
However, while insisting that he did not want to assume the mantle of a Parliamentary champion of gay rights, Mr Twigg said he did believe there was a ground-swell of sympathy in Parliament.
"I will play my part, but I'm confident that the majority of my Labour colleagues will play their part as well."
Mr Twigg stopped short of urging other MPs who were homosexual to acknowledge publicly their sexuality.
He said: "Obviously I would prefer that MPs would come out, but that has to be a matter they decide for themselves. I believe that's a matter of personal choice."
Stonewall's new campaign - Equality 2000 - aims to enhance gays' rights in key areas by the end of the century.
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