Pakistan's Prime Minister Raja Pervez Ashraf agreed at a Supreme Court hearing Tuesday to reopen graft investigations into the country's president, a move that could reduce tensions between the country's judicial and executive branches.

The Supreme Court has been trying for years to pursue a corruption investigation of President Asif Ali Zardari. Earlier this year, it found former Prime Minister Yousuf Raza Gilani in contempt of court for failing to act on a court order to start a graft probe of the president, a decision that...