Gov.-elect Dan Malloy said Tuesday that U.S. Sen. Joe Lieberman should be congratulated for his role in repealing the military’s “don’t ask, don’t tell” policy on sexual orientation, but Malloy wouldn’t go any further than that with respect to his support for the senator.

The question was posed during a news conference Tuesday. Malloy was asked whether Lieberman should be the nominee for his Senate seat in 2012.

“Only if he was to win the nomination,” Malloy said.

Lieberman’s future has been the subject of discussion recently. He won re-election as an independent in 2006, launching the Connecticut for Lieberman Party. And he hasn’t yet committed to seeking the Democratic Party’s nomination in 2012.

As the newly elected Democratic governor, Malloy has become the defacto head of the Democratic Party in the state, even though Nancy DiNardo likely will remain, with Malloy’s blessing, as the chairwoman.

But the former Stamford mayor remained on the fence with respect to Lieberman.

“I’m not going to comment on that race at this time,” Malloy said. “I do want to say that I appreciate his leadership in bringing about what I thought was an historic moment in the United States Senate where “don’t ask, don’t tell” is on the road to appropriate extinction. I applaud Joe and Chris and every United States Senator who voted for removing that scar on our road to human rights in this state, in this nation.”

He also applauded the newest members of his administration, Rep. Michael Lawlor and Sen. Andrew McDonald, for their efforts as co-chairmen of the legislature’s Judiciary Committee in moving toward same-sex marriage equality — a decision which was ultimately decided by the state Supreme Court.

Malloy said his good friends U.S. Reps. Joe Courtney and Chris Murphy are considering a run for Lieberman’s seat, so he is not ready to weigh in on the 2012 U.S. Senate race just yet.

“We’ll cross that bridge when we get to it,” Malloy said.

Lieberman, who supported the Defense of Marriage Act in 1996, carried the DADT legislation across the finish line this past weekend, but it wasn’t enough to help win him back the support of the Democratic base.

His support for civil rights has been a mixed bag for the Democratic Party faithful.