ST. PAUL  — Ramsey County leaders upped their offer Thursday to be the home of a new Minnesota Vikings stadium to a total of $375 million, while the city of Minneapolis offered $313 million for the team to rebuild at the current Metrodome site.

The two local governments submitted dueling proposals Thursday to Gov. Mark Dayton as each seek to host a new stadium. Ramsey County board members want to build in suburban Arden Hills, north of St. Paul, while Minneapolis Mayor R.T. Rybak is trying to keep the team in his city’s downtown.

Dayton, who supports the team’s push for a public subsidy to replace the Metrodome, had set Thursday as the deadline for the proposals as he and lawmakers look to vote on a package in the upcoming legislative session.

Ramsey County leaders said they could raise $24 million a year with the addition of a 3 percent sales tax on food and liquor. The Minneapolis plan calls for raising $6.5 million a year for 30 years, plus $150 million for construction, from sales taxes already in place.

Vikings Vice President Lester Bagley said Thursday that the team continues to prefer the Arden Hills deal, but did not close the door on Minneapolis and said ultimately the team would build wherever the Legislature decides.

“We have our preference, but we need to resolve this issue,” Bagley said. “If this does evolve into a Minneapolis site, we want to make sure the site dynamics and costs are taken into consideration and the local finance proposal has support and the votes to pass at the Capitol.”

Neither proposal submitted Thursday included major changes from what had been offered earlier. And Rybak, while stressing the Metrodome site remains the favorite of city leaders, said they were still open to an alternative location on the opposite side of downtown if Vikings owners can’t overcome their qualms about the Metrodome site. Building there would force the team to play on the University of Minnesota campus for three seasons, which its owners say would drain profits.

In addition, stadium boosters in both Ramsey County and Minneapolis face potential stumbling blocks. The efforts of Ramsey County leaders have inspired a petition drive that seeks to block stadium-related tax increases at the county ballot box this November, while Rybak would have to push his proposal through a reluctant city council and around a provision in the city’s charter that forbids spending more than $10 million in city money on a stadium project.

“I think if we’re going to raise that amount of public money, there are priorities that would be better investments — education and infrastructure come to mind,” said Minneapolis City Councilwoman Betsy Hodges.

She pointed out the last time Minneapolis residents voted on a stadium matter was 1997, when they overwhelmingly passed the charter amendment with the $10 million limit on city investment in a stadium. If the stadium is to be in Minneapolis, state lawmakers would likely be forced to pass an exemption to that.

Both Hodges and Councilman Gary Schiff, another opponent of a city subsidy, said they didn’t know if a majority of their colleagues would ultimately back Rybak’s push. “It’s been difficult to count votes because we don’t know from day to day what exactly the proposal is,” Schiff said.

Rybak acknowledged an uphill battle with the city council, but said the proposal finalized Thursday would sweeten the deal by diverting a part of the targeted sales tax proceeds not just to a football stadium but to a Target Center renovation that would free up city property tax dollars that now go to that NBA arena.

“We believe this plan can pass the city council,” Rybak said. “It’s a tough vote, but that’s proven to be the case any time the Legislature or a public body has to take a vote on a stadium.”

Ramsey County stadium backers have their own political complications. While commissioners Rafael Ortega and Tony Bennett sold the Arden Hills site as offering the most land — and potential for future adjacent development — they must contend with the efforts of a group of citizens and local government officials circulating a petition for an amendment on November’s ballot that would prevent the county board from approving any tax money for a stadium without a public vote of citizens.

“The people in Ramsey County are very disappointed that a couple of our county commissioners are trying to ram this down our throats without the consent of the people,” said Ady Wickstrom, a councilwoman in the Ramsey County city of Shoreview who’s helping lead the petition drive. She said in a matter of days, her group has collected about 2,000 of the roughly 17,000 signatures they think they need to qualify it for the November ballot.

“People are flocking to sign it,” she said.

Bennett and Ortega refused to acknowledge the petition drive as a possible roadblock. “That doesn’t have anything to do with us,” Bennett told reporters after dropping off the Ramsey County proposal at Dayton’s office.

Just a day ago, a third potential host community came out of the woodwork. The newly elected mayor of Shakopee, a suburb south of Minneapolis, said his community — home to an amusement park, a horseracing track and other entertainment destinations — would be a great stadium site. But Vikings officials said the offer was coming too late to get serious consideration.

At his news conference, Bagley said the team hoped to have a single legislative proposal, with one specific site and a specific financing proposal, in the next week to 10 days.