CAIRO, July 3 (Reuters) - Egypt's second-biggest Islamist party said on Wednesday it agreed to an army political "road map" that suspends the constitution so that the country can avoid conflict.

The road map appoints the head of the constitutional court as interim head of state, replacing the Muslim Brotherhood's President Mohamed Mursi.

"We took this position and we took these decisions only so we stop the bloodshed of our people," Galal Murra, Nour's secretary general, said in a televised broadcast. (Reporting by Tom Perry and Shadia Nasralla; Writing by Alexander Dziadosz)