Video (01:21) : Hundreds of gay marraige supporters rallied at the State Capitol to support marriage equality.

Gov. Mark Dayton made an impassioned case Thursday that same-sex couples should be allowed to marry in Minnesota, kicking off a frigid outdoor Capitol rally that intensified pressure on legislators to pass a marriage measure.

“Yes to marriage, yes to same-sex marriage, yes to the constitutional right, the American right, to marry the person you love,” Dayton told hundreds of cheering supporters.

The DFL-controlled Legislature is weeks away from voting on a measure that would make Minnesota the 10th state to legalize same-sex marriage. Legislators are grappling with the issue as the U.S. Supreme Court takes a closer look at restrictions on same-sex marriage.

Dayton dismissed a last-ditch proposal by opponents of same-sex marriage to offer gay and lesbian couples the protection of civil unions.

“People don’t want to be civil unioned, they want to be married,” Dayton said.

The governor urged supporters to meet with legislators and “be respectful, but be persuasive.”

“Yes to constitutional right, the American right, to marry the person you love,” Gov. Mark Dayton told the crowD rallying Thursday to legalize same-sex marriage.

Right now, neither side is declaring victory, and those involved believe the margin will be only a couple votes. That has both sides frantically meeting with undecided legislators.

Minnesotans United for All Families, the group leading the push to legalize same-sex marriage, held the rally as a show of force, to persuade those final few undecided legislators that momentum is on their side.

Minnesota for Marriage, the main group trying to block gay marriage, is mounting its own campaign to urge legislators to keep the state’s marriage law as it is.

It is continuing its statewide bus tour this weekend with stops in Eden Prairie, Owatonna, Rochester and Austin. The group held events in northern Minnesota last weekend and even tried to stop by the homes of several legislators.

Autumn Leva, a spokeswoman for Minnesota for Marriage, said it has persuaded at least a couple of legislators just this week to vote with its supporters. “We are working hard every day,” she said. Leva would not name the legislators meeting with the group.

Ken Martin, chair of the Minnesota DFL Party, said passing same-sex marriage is crucial to energizing DFL activists in the upcoming election.

“I absolutely think our base would feel disillusioned we didn’t move on full marriage equality this year,” Martin said.

Rep. Tim Faust, DFL-Hinckley, has been one of the most watched members of the House on the marriage issue. He’s an undecided DFLer from a largely rural area that voted overwhelmingly for an amendment in November that would have banned same-sex marriage in the state Constitution.

A week ago, Faust had told a group of gay marriage opponents that he was unsure how he would vote.

On Thursday, Faust said for the first time that he is leaning toward legalizing same-sex marriage — even if many of his constituents disagree.

Faust stood to the side of the rally Thursday, unprotected from the sleet and rain. He said nearly all the arguments against same-sex marriage are biblical but noted that many devoted people view it the other way.

“Then the question becomes, do we have the right to impose our religious belief on others?” Faust asked. “If the reason we are arguing we shouldn’t be doing this is because of religious beliefs, it’s pretty hard to make that argument.”

Moments later, state Rep. Karen Clark walked up to Faust. The Minneapolis DFLer is a lead sponsor of the same-sex marriage legislation.

She locked arms with Faust and smiled. Then the two walked though the driving sleet back to the Capitol.