All are male.
Senators in the group include Finance Committee Chairman Orrin Hatch, Health and Education Committee Chairman Lamar Alexander and conservatives Ted Cruz and Mike Lee.
A GOP aide defended the makeup of the group.
"We have no interest in playing the games of identity politics, that's not what this is about; it's about getting a job done," the aide said. "We'll work with any member of any background who wants to pass a health reform bill that will reduce premiums and take away the burdens that Obamacare inflicted.
"To reduce this to gender, race or geography misses the more important point of the diverse segments of the conference the group represents on policy -- from members who support Medicaid expansion, to those opposed to it, to those who have called for long term full repeal," the aide added.
The announcement of the health care working group is yet another signal that the bill passed out of the House is merely a starting point for Senate Republicans, who have been saying for months that they had serious concerns about the House's efforts to repeal Obamacare ranging from how the House bill dealt with Medicaid to how it handled people with pre-existing conditions.
Even as the legislation was passing on the House floor, Senate Republicans were admonishing the House's efforts.
"A bill -- finalized yesterday, has not been scored, amendments not allowed, and 3 hours final debate -- should be viewed with caution," tweeted South Carolina Sen. Lindsey Graham
Here are the group of 13 Republicans who will work to build the Senate's bill:
Members of Senate leadership
Majority Leader Mitch McConnell of Kentucky
Sen. John Cornyn of Texas
Sen. John Thune of South Dakota
Sen. John Barrasso of Wyoming
HELP Chairman Lamar Alexander of Tennessee
Budget Chairman Mike Enzi of Wyoming
Finance Chairman Orrin Hatch of Utah
Sen. Ted Cruz of Texas
Sen. Mike Lee of Utah
Sen. Tom Cotton of Arkansas
Sen. Cory Gardner of Colorado
Sen. Rob Portman of Ohio
Sen. Pat Toomey of Pennsylvania
This story has been updated.