CAIRO — An industrialist who rose to prominence during the Mubarak era was named as Egypt’s new prime minister on Tuesday, a day after his predecessor abruptly announced the resignation of the military-backed government that had managed the country since July.

The new prime minister, Ibrahim Mehlib, who headed a state-owned construction company and served in the last cabinet as housing minister, said at a news conference that he would name a new government within days. It will focus on improving living conditions, defeating terrorism and ensuring a smooth presidential election, which is expected to be held in the coming weeks, he said.

Egypt’s popular military chief, Field Marshal Abdul-Fattah el-Sisi, is widely expected to enter the race, and he is already considered the front-runner.

Mr. Mehlib is the sixth person to occupy Egypt’s often thankless post of prime minister since the uprising against President Hosni Mubarak three years ago, a period that saw the country’s challenges turn into crises that seemed to defy government solutions. The sense of crisis deepened even further in July, when the military ousted the Islamist president, Mohamed Morsi, setting off months of bloody civil strife.