Hughes also alluded to Brown's upset win in 2010.
"We shocked the world in 2010, and united, we can do it again," she said.
Rob Collins, executive director of the National Republican Senatorial Committee, said it was time for the party to move forward after Brown's announcement. He predicted a nasty Democratic primary between Lynch and Markey and said the GOP was intent on defeating "whichever career politician limps through."
Massachusetts Democratic leaders expressed confidence they would keep Kerry's former seat.
Markey and Lynch both issued statements Friday saying they understood and respected Brown's reasons for not getting into the race.
Weld recently returned to Massachusetts to join a Boston law firm and had said he would consider a run for the Senate if Brown did not. Weld did not return a call seeking comment on Friday.
A message was also left with Healey, who served as lieutenant governor from 2003-2007 under then-Gov. Mitt Romney and lost the governor's race to Democratic Gov. Deval Patrick in 2006.
Winslow, a former judge and chief legal counsel in Romney's administration, said in a statement that he would reflect over the weekend on whether to run, weighing family considerations and "whether there is room in the national Republican Party for a member who is both fiscally prudent and socially tolerant."
Tisei ran unsuccessfully for the U.S. House last year against Democratic Rep. John Tierney. He said Friday he was surprised by Brown's decision and would discuss his options with family, friends and supporters in the coming days.
Candidates will have a tight window — about four weeks — to gather the required 10,000 signatures to get their names on the primary election ballot.
The general election is scheduled for June 25.
The winner of the special election would have to face voters again in November 2014, when Kerry's six-year term would have expired.
Patrick this week named William "Mo" Cowan, a former top aide, to fill Kerry's seat on an interim basis until the election.
Associated Press reporter Steve LeBlanc contributed to this report.