ROSEVILLE — Minnesota Senate Republicans elected Dave Senjem of Rochester as their new majority leader Tuesday to replace Amy Koch, who resigned amid revelations she had an inappropriate relationship with a Senate staffer.

GOP senators announced their choice of Senjem and an all-new leadership team after meeting for more than 10 hours at a suburban Minneapolis motel. Senjem acknowledged that the last two had been difficult, but said Republicans are now united in looking ahead to the 2012 legislative session and elections. All 67 Senate seats will be up for grabs next year.

“Our priorities have not changed: it’s jobs and the economy, it’s reforming government, it’s being good stewards of the taxpayers’ dollars,” Senjem told reporters as most of his 37-member caucus looked on, minus Koch and her former leadership team.

Koch, R-Buffalo, publicly admitted to the relationship last Wednesday. She gave up her leadership post Dec. 15, one day after she was confronted by her colleagues about the relationship. She has said she would not run for re-election, but she remains a senator. She attended Tuesday’s caucus meeting but left before the news conference Tuesday night.

Along with the speaker of the House, the Senate majority leader is among the most powerful positions in state government. He or she wields considerable authority in deciding which bills get considered and which are left to languish in committee.

Democratic Gov. Mark Dayton, who struggled to reach compromises with the GOP-controlled Senate and House on spending levels last session and couldn’t get them to agree to raise taxes to balance the budget, said he called Senjem to congratulate him.

“I look forward to a constructive working relationship with him on behalf of the people of Minnesota,” Dayton said in a statement.

Senjem, 69, unsuccessfully challenged Koch for the majority leader’s post last December. He’s seen as a moderate known to have good relationships with Democrats. He was first elected in 2002, and served as minority leader from 2007 until a new Republican majority took power last January. The married father of two is a retired environmental affairs officer for the Mayo Clinic.

Elected as assistant majority leaders were Sens. Roger Chamberlain of Lino Lakes, Paul Gazelka of Brainerd, Ted Lillie of Lake Elmo and Claire Robling of Jordan. Caucus bylaws also give Senjem a week to appoint two more assistant leaders. Robling called Senjem a “great collaborator” who will listen to input from other caucus members.

The politicking over potential successors to Koch took place largely in private, and it wasn’t immediately clear which other senators ultimately became candidates. Senjem declined to say, but said that only one ballot was taken during the long meeting.

Neither Koch nor other GOP senators have publicly named the Senate employee with whom she was involved. But on the day her resignation was announced, other Senate Republicans announced that caucus spokesman Michael Brodkorb, one of Koch’s chief aides, was no longer employed by the Senate. Brodkorb has not publicly commented on the reasons for his departure either, but he has hired a lawyer.

The new majority leader must try to unite a caucus that’s still reeling from the scandal, with the Jan. 24 opening of the legislative session quickly approaching. The session could be dominated by the Minnesota Vikings’ quest for partial public funding for a new football stadium, an issue on which lawmakers of both parties are split.

Senjem’s election is seen as good news for stadium proponents because he’s considered more open to gambling as a funding source than other senators interested in the job. But Gazelka, one of the assistant majority leaders, said the stadium was not an issue at Tuesday’s meeting.

Republicans have held the majority in the Senate only since last year, when the GOP took control of both chambers. All their seats will be on the ballot in 2012, including several held by GOP freshmen from swing districts.

Further clouding GOP prospects for 2012, the state party organization is in disarray. It’s still somewhere between $500,000 and $1.2 million in debt after the 2010 election. The party’s chairman, deputy chairman and executive director all have left in recent weeks.