The announcement follows controversy over a leaked government report that sought to review religious protections, which at present allow schools in most states to reject gay students.
Fairfax Media, which obtained a copy, had said the report recommended the rule be applied nationwide, and also include discrimination based on gender identity and relationship status.
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Leak caused 'confusion'But Morrison rejected the recommendation, and criticized the leak for creating "unnecessary confusion and anxiety for parents and students alike."
"I will be taking action to ensure amendments are introduced as soon as practicable to make it clear that no student of a non-state school should be expelled on the basis of their sexuality," he said in a statement.
Morrison said his government does not support expulsion of students from religious non-state schools on the basis of their sexuality and that he believed most MPs agreed with his stance.
"I also know that this view is widely shared by religious schools and communities across the country," he added.
The controversial review was ordered after Australia, last year, legalized same-sex marriage, after conservatives complained that the change would restrict religious freedoms.
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By-election next weekThe discrimination issue has come to the fore ahead of a crucial by-election for Morrison's ruling Liberal-National coalition in the vital Sydney seat of Wentworth on October 20.
Australian public broadcaster, ABC, cited government insiders saying they were concerned about the Liberal Party's prospects of holding the seat vacated by former Prime Minister Malcom Turnbull.
At least one opposition politician, meanwhile, called for the planned law to go further, to cover discrimination against LGBT teachers and other staff.
Meanwhile, a study of high school students found the majority of young Australians do not support religious exemptions.
Eighty-four percent of 1,200 teenagers interviewed last year believed students should be allowed to openly express their sexual or gender identity, according to data compiled by three top Australian universities.
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