Senate President Therese Murray on Wednesday formally threw her support behind Attorney General Martha Coakley’s gubernatorial campaign, saying she was confident that Coakley’s campaigning skills had improved since her ill-fated 2010 Senate run.

“We talked about that, but I also feel that after the primary last time that there were individuals that should have come together – you know that unity thing we do? – that didn’t necessarily do that. Where they did for Liz Warren, they didn’t do it for Martha Coakley. And I think that was one of the reasons she did not win.”

Murray said that Coakley could lose the party’s June nominating convention to Treasurer Steven Grossman, but suggested her work as attorney general would persuade Democrats to rally to her cause.

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“She sticks her neck out, that’s why I like her,” Murray said during an interview in her office.

Murray said she was undecided about her own immediate political future. Senate President Pro Tempore Stanley Rosenberg, who has claimed the votes sufficient to succeed Murray, has endorsed Grossman. Murray said she would decided whether to run again for her Senate seat “in the next few weeks.”

“I haven’t finished those discussions,” she said.

Murray, a former budget committee chair who has been mentioned as a potential administration and finance secretary in a Democratic administration, said she did not plan to exert pressure on her fellow senators but wanted to have a greater say in the Coakley campaign than she did in 2010.

“I would like to think I would be consulted more about what their moves are going to be than the last time,” she said.

“We had some very frank discussions,” she said of her discussions with Coakley.