Gay marriage 'will cause us problems': Abbott

A key Senate crossbencher says the Prime Minister Tony Abbott counselled him against introducing a same-sex marriage bill because it could cause more trouble for the government.

"His argument was that the government's got enough troubles without this one coming along," Liberal Democrat Leyonhjelm told reporters.

Mr Abbott had made plain his opposition to legalising gay marriage during a recent meeting with the senator about his private bill due to be introduced to parliament on Wednesday.

The prime minister's preference was for the bill to be abandoned, rather than allow it to proceed once coalition MPs were allowed a conscience vote, Senator Leyonhjelm said.

Mr Abbott conceded no ground on allowing a conscience vote during the meeting.

But Senator Leyonhjelm thinks there's enough support inside the coalition for one to occur.

"There's some people I think will become quite vocal if they're not allowed a conscience vote," he said.

Communications Minister Malcolm Turnbull was among those who support a free vote, he said.

A private bill legalising gay marriage, sponsored by Labor MP Stephen Jones, was defeated in 2012.

Senator Leyonhjelm believes the government is more likely to be open to a bill brought by a libertarian.

He intends waiting for sufficient support before seeking a vote.

The bill will allow non-government religious and civil celebrants the right to refuse to marry gay couples.

The Greens say they will vote for marriage equality and urged Mr Abbott to allow a conscience vote.

Comment was being sought from the prime minister.