The legalisation of same-sex marriage has moved a step closer after the Senate effectively passed a same-sex marriage bill for the first time in Australian history on Tuesday.

The bill breezed through its second-reading stage, and every amendment from Coalition senators was defeated in a debate that lasted late into the night.

A proposal allowing civil celebrants to refuse to perform gay weddings - backed by Attorney-General George Brandis and Resources Minister Matt Canavan - was rejected 25 to 38 just after 11pm.

Labor had earlier in the day announced it would vote as a bloc against all amendments, including those from the Greens, One Nation and David Leyonhjelm to be debated on Wednesday.