ST. PAUL — A Democratic state senator who holds what many have seen as a swing vote on Minnesota’s gay marriage bill said Tuesday that he will vote to legalize it.

Sen. Kent Eken, who represents a northwestern Minnesota district where 53 percent of voters backed last fall’s failed bid to outlaw same-sex marriage, said he came to his decision to support the current gay marriage bill after hearing from many constituents. Among them were straight and gay couples who fervently support same-sex marriage rights, and many opponents he said are resigned to gay marriage becoming legal.

“People are just becoming more accepting of it,” Eken said. “Even among many who are against it, there’s a feeling that it’s inevitable, that it’s going to happen.”

Eken, an educator and married father of four from the town of Twin Valley, represents a district that includes the city of Moorhead and small rural communities near the North Dakota border. He said his constituents are more concerned about schools, roads and bridges, and nursing homes and hospitals than they are worried about legal gay marriage.

Eken was seen as a swing vote because of the makeup of his district and because a few weeks ago, he was one of four Democrats who sided with Senate Republicans in a failed attempt to stall the gay marriage bill. Eken said he was still undecided at the time and only voted the way he did because he wanted the Legislature to make more progress on assembling the state budget before taking up gay marriage.

Minnesota lawmakers could vote soon on a bill to gay marriage legal starting Aug. 1. The first vote would likely come in the state House.