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But he also waded into two state Senate recall elections in Colorado that were prompted by a backlash to new gun control legislation. Both candidates lost.

Colorado Gov. John Hickenlooper, a Democrat, recently told USA Today that it’s “probably not a bad idea” for groups such as Mr. Bloomberg’s to stay away from a would-be recall election involving state Sen. Evie Hudak, a Democrat.

“I do think that, again, getting the real facts out on some of these issues — I mean, universal background checks is not the ‘ogre,’ it’s not the evil, demonic taking of guns that it’s been presented as,” Mr. Hickenlooper said.

In 2007, Mr. Bloomberg campaigned for former state Sen. Jeannemarie Devolites Davis, a Republican from Northern Virginia, in her unsuccessful re-election bid against Democrat J. Chapman “Chap” Petersen of Fairfax.

“This may be an effort to put a win in Bloomberg’s column by entering the political discussion in Virginia,” said Stephen Farnsworth, a political science professor at the University of Mary Washington. “But the polls show that long before we heard of Michael Bloomberg, there was a significant gap favoring McAuliffe. There’s an old saying: ‘Victory has a thousand fathers.’ And I think Bloomberg wants to be one of them.”

Mr. McAuliffe has held a modest but steady lead in the Virginia race, though a poll released Tuesday by Rasmussen Reports gave him a 17-point edge over Mr. Cuccinelli, 50 percent to 33 percent.