It is the 14th attempt to pass such laws in the state.
The bill, introduced jointly by Labor MP Steph Key and Liberal MP Duncan McFetridge, will be subject to a conscience vote by both major parties.
A conscience vote on the bill is due to be held on Thursday.
The Victorian Labor government is also poised to introduce similar laws, while in Western Australia a recent case has sparked renewed debate.
Turnbull government minister Arthur Sinodinos said on Sunday the SA bill was a matter for South Australia and didn't think the federal government would intervene.
