Yemeni President Ali Abdullah Saleh has accepted a political deal brokered by neighboring Arab countries that would have him step down from power after 30 days in exchange for immunity for himself and his close relatives, according to a presidential aide.

The apparent softening of the longtime ruler's recalcitrant stance that he would remain in power until the end of his term in 2013 comes after a burst of arm-twisting and backroom diplomacy by Yemen's close allies Saudi Arabia and the United Arab Emirates. It renews the possibility...