After slashing the number of drilling rigs for months, U.S. shale-oil companies say they are ready to bring rigs back into service, setting up the first big test of their ability to quickly react to rising crude prices.

Last week, EOG Resources Inc. said it would ramp up output if U.S. prices hold at recent levels, while Occidental Petroleum Corp. boosted planned production for the year. Other drillers said they would open the taps if U.S. benchmark West Texas Intermediate reaches $70 a barrel. WTI settled at $60.50 Wednesday,...