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Mr. Bloomberg fared better Tuesday in Virginia, where he contributed nearly $2 million to help elect Democrat Terry McAuliffe as governor.

Stu Loeser, spokesman for Independence USA, a Bloomberg-financed political-action committee, said the mayor has no intention of stepping out of the political arena, especially when it comes to cracking down on firearms.

“We’ve done it in New York, we can do it in other places, and Michael Bloomberg is going continue to help candidates across the country who support commonsense gun laws,” Mr. Loeser said in a conference call. “He’s going to help them get their message out. The specifics of what that means are things you will see over the next weeks and months, more like months and year.”

Before plowing more money into Colorado, however, analysts say Mr. Bloomberg may want to think twice, or at least make his contributions less transparent.

“He’s been rejected three times in Colorado. I don’t know what interest he has here,” said GOP state Rep. Frank McNulty. “But if he’s going to continue to put his name behind his millions, I think that’s good for Republicans.”