Tasmania's Liberal-led lower house of parliament has thrown its support behind marriage equality, increasing pressure on Canberra ahead of a planned national plebiscite.

It became the third state assembly to pass a motion supporting legalisation of same sex marriage, voting 15-9 in favour.

Tasmanian Premier Will Hodgman. Credit:Rob Blakers

Introduced by the Greens, the motion won the support of Liberal MPs including Premier Will Hodgman and Deputy Premier Jeremy Rockliff.

It follows similar motions being passed by Coalition-dominated parliaments in NSW and Western Australia.