An Indian transgender couple who both underwent sex re-assignment have tied the knot in a traditional Bengali ceremony, in what is believed to be the state's first "rainbow wedding".

Surrounded by family and friends, bride Tista Das, 38, and groom Dipan Chakravarthy, 40, took part in rituals and pledged their love for each other in Kolkata, the capital of West Bengal state.

"We are feeling awesome actually. We are out of the gender box and we love to be an exception and we think this is a strong bond between us," Tista Das told AFP on Monday.

"It's a bond of love. It's a bond of liberty also," she said. "And this is the solidarity of our souls."

Das said she battled for a long time to "achieve her identity as a woman, as a human being", adding: "I was not even considered as a human being in this brutal society."

A transgender friend of the couple, Anurag Maitrayee, said the ceremony was a "beautiful, emotional union of two hearts and two souls".

"Despite all the oddities and all the atrocities, I have seen how Tista and her journey from a man into a woman and her relation, emotion, love with a person with a soul whose journey is from a woman to a man," Maitrayee said.

Official estimates for India's transgender population are not known but they are thought to number several million.

Transgenders often live on the extreme fringes of Indian society, with many forced into prostitution, begging or menial jobs.

Over the centuries transgenders have assumed different roles in society, from royal courtesans to participants in birth ceremonies and other auspicious occasions.

They have waged a lengthy battle to protect their rights and end discrimination.

India's Supreme Court recognised them as a third gender in a historic 2014 ruling.

On Tuesday, India's lower house passed a transgender bill to enshrine the rights of transgender people in law. The bill is currently being discussed in the upper house.

But the community as well as human rights activists have raised concerns that the bill's language is unclear over whether it allows transgender people to self-identify.

"The Transgender Persons Bill should be a remarkable achievement for a long-persecuted community, but the current draft fails on the fundamental right to self-identify," Human Rights Watch South Asia director Meenakshi Ganguly said last month.

"It's crucial that the law be in line with the Supreme Court's historic ruling on transgender rights."

(With inputs from AFP)