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A Senate inquiry into equal marriage has moved the issue a step closer as it unanimously rejected several measures to discriminate LGBT people.

The report by the committee that was released on Wednesday examined the Government’s bill and rejected a number of proposals, including the ability for civil celebrants to reject marrying a same-sex couple.

In the report, it recommends creating a new category of independent religious celebrants who, because of their religious beliefs, would be allowed to refuse to marry a couple.

However, it did state this should be reviewed and more clearly defined in order to get a better balance between freedom of religion and equality.

Civil celebrants would have no form of objection and would be required to marry any couple legally allowed to do so.

The inquiry also recommended removing the ability for anyone to reject a same-sex wedding on the basis of “conscientious objection”, stating it was “unprecedented” to allow one group of people to justify discrimination against another.

Most marriage equality advocates welcomed the news and hoped it raised the chance of cross-party cooperation in this session of Parliament.

Marriage advocate, Rodney Croome, said the report rejected, “proposed discrimination against same-sex couples [and] shows progress on marriage equality is possible when our elected members work across party lines”.

Anna Brown the chair of Australians for Equality told the Guardian the report offered “sensible solutions to address concerns about religious freedom”.

The committee was chaired by marriage equality opponent David Fawcett and included the pro-marriage equality Liberals Dean Smith and James Paterson, Labor, the Greens and the Nick Xenophon Team.

Recently, an Australian politician claimed that LGBT people were using Nazi mind control to increase support for same-sex marriage.