Pressure is mounting on the Liberal Party to allow a free vote on same-sex marriage, with libertarian senator David Leyonhjelm saying it was time for government MPs to discuss the matter.

Senator Leyonhjelm will make his second-reading speech on his "freedom to marry" bill next Thursday, and says that the Liberal Party should decide whether it will allow a free vote on the issue at their party room meeting next Tuesday.

He said this meant Prime Minister Tony Abbott could not "stand in the way".

"The time has come for the Prime Minister to reveal whether the word 'liberal' actually means anything to him or it's just a brand name like Datsun or Krispy Kreme," Senator Leyonhjelm said.