The storm was 118 miles south-southwest of the fishing village of Puerto Angel in southern Oaxaca state and nearly stationary with maximum sustained winds of 40 mph.
It was unclear whether Barbara would turn toward land or head out to open sea after strengthening, but people living along the western coasts of Mexico and Guatemala should monitor the storm in any case, the hurricane center said.
Barbara follows Alvin, the first tropical storm of the eastern Pacific's 2007 season. It formed Monday but was downgraded Tuesday to a tropical depression as it headed away from land. Two eastern Pacific storms in May is unprecedented — the hurricane center has named only two May storms in the past, in 1984 and 1956.