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Mr. Brown has not ruled out a run for governor against Mr. Patrick in 2014.

Rob Collins, executive director of the National Republican Senatorial Committee, said in a statement, “This was no doubt a tough personal decision for Senator Brown and his family, who understandably need to recharge after several long, hard-fought campaigns. … The Republican conference remains excited about the prospect of the Massachusetts special election, and we have the organization, energy and resources to win.”