The plan would create gender-neutral national regulations on marriage, allowing local parishes to unite same-sex couples if they wish, The Local reported. It would also give gay couples the right to adopt children and allow gay women to have children by artificial insemination.
The Christian Democrats have pledged to continue to oppose gay marriage.
"My position is that I have been tasked by the party to argue that marriage is for men and women," the party's leader, Goran Hagglund, said Saturday in an interview on Swedish Radio. "When we discuss it between parties we are naturally open and sensitive to each other's arguments and we'll see if we can find a line that allows us to come together."
Sweden has seven political parties with a four-party Alliance currently controlling parliament.