A clear majority of voters in key Coalition-held seats support MPs having a free vote on same-sex marriage, according to a new poll.
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A ReachTEL survey of four federal seats, including one of the country's most marginal, has found that between 64 and 69 per cent of voters back a free vote for all MPs.
The results come as Coalition MPs gather for their regular sitting week meeting on Tuesday. And as Labor leader Bill Shorten and Greens leader Richard Di Natale continue to pressure Prime Minister Tony Abbott to smooth the way for a free vote for Liberal MPs on same-sex marriage.
In Michelle Landry's Queensland central coast seat of Capricornia (held with a margin of just 0.8 per cent), the poll found 64 per cent of voters surveyed supported a free vote. A further 21 per cent opposed the idea and 15 per cent were undecided.
In Jason Wood's marginal outer Melbourne seat of La Trobe (held by 4 per cent), almost 67 per cent back a free vote, with 18 per cent opposed and 15 per cent undecided.
The safe Gold Coast seat of McPherson (held by Karen Andrews with a margin of 13 per cent), 69 per cent of voters support the free vote, 20 per cent are opposed and 11 per cent are undecided.
In the northern NSW seat of Lyne (safely held by David Gillespie on 14.8 per cent), almost 65 per cent support a free vote, with 21.7 per cent opposed and 13.7 per cent undecided.
The poll was conducted for Australian Marriage Equality on Sunday, which polled between 670 and 690 voters per seat. The four seats were chosen because the local members had indicated they wanted to hear from their constituents or were key regional seats.
"The message for Tony Abbott is to allow a free vote as soon as possible if he wants to keep the Coalition's stocks high [in] seats he needs to stay in government," Australian Marriage Equality national director Rodney Croome said.
"These key seats want a free and open debate on marriage equality, and don't want their MP restricted by party line."
When asked on Monday if he thought most Australians supported same-sex marriage, Mr Abbott replied: "Let's see where the community debate goes."
The most commonly cited general opinion poll on same-sex marriage was done by the Liberal Party's pollster Crosby Textor last year. It found 72 per cent of those polled supported same-sex marriage.
While one Coalition MP said it was "always possible" same-sex marriage would be raised in Tuesday's meeting, it is considered unlikely.
Many senators are away for Senate estimates hearings and Mr Abbott has stressed that "every single one of us on the Coalition side" would be focused on the budget for the next few weeks.
However, first-term Liberal MP Sarah Henderson announced on Monday night that she supported same-sex marriage, "in anticipation that the issue of marriage equality may come before the Coalition party room tomorrow morning".
Ms Henderson, who holds the seat of Corangamite that takes in Geelong, called for a cross-party bill to be brought before the Parliament.
"Support for marriage equality is consistent with fundamental Liberal values, which embrace freedom of the individual and stable, long-term relationships," she said in a statement.
