John Kasich thanked supporters at a Super Tuesday rally in Mississippi.
Kasich, the governor of Ohio, has been trying to build off his surprising second-place finish in the New Hampshire primary last month.
As of 11 p.m., he has yet to win any states. His speech Tuesday was full of family remembrances and tributes to his supporters but very little discussion of the night's results.
Donald Trump captured Georgia and other states. Some states remained too close to call.
He has resisted calls from some other Republican power brokers to drop out of the race.