Nearly two thirds of Danes support a call to allow gay and lesbian couples to be married by the Church, according to a poll on Wednesday.
Denmark was the world's first country to allow a civil union for homosexuals, in 1989, but its parliament is now split over a move by the centre-left opposition to amend the law to allow religious weddings too.
The minister for religion Birthe Roenn Hornbech has urged lawmakers to think the question through in-depth before reaching any decision.
But according to a poll published by the Christian daily Kristelig Dagbladet on Wednesday, 63 percent of the Danish population would be happy to see gay couples married at the altar.
A quarter of respondents said they would oppose the move, while 12 percent gave no opinion, according to the Capacent Research poll of 1,304 people carried out of March 5.
Separately, the Berlingske Tidende daily found that six out of 10 bishops with the Danish Evangelical Lutheran Church would agree to see gay couples make their vows in Church.
Denmark's civil partnership, since emulated across much of the Western world, grants homosexual couples most of the same rights as heterosexuals but gay Christians have continued to lobby for the right to a Church marriage.
In 1997, Denmark's bishops agreed to a compromise allowing for civil unions to receive the blessing of the Church but omitting the key phrase "Will you take this man (woman) to be your husband (wife)" from the ceremony.