ISLAMABAD—Pakistan army chief Gen. Raheel Sharif strengthened his authority on Monday as he named a new head of the Inter-Services Intelligence agency, a key political and security post, and made a raft of other senior appointments.

Gen. Sharif became army chief in November, and the new appointments—made to replace retiring generals—allow him to put his own men in crucial positions as a political crisis continues to grip the civilian government of Prime Minister Nawaz Sharif amid protests demanding his resignation.

The new head of the ISI will be Lt. Gen. Rizwan Akhtar, who has just completed a stint as head of the paramilitary Rangers force for the southern province of Sindh. As the Rangers chief, he has won praise for his leadership of the operation launched a year ago to clear Karachi of the militants and criminals who have turned Pakistan's biggest city into a chaotic and dangerous place.

The army is engaged in an operation, launched in June, to fight Taliban and al Qaeda militants in the North Waziristan tribal areas along the Afghan border.

Gen. Sharif and the prime minister, elected in May 2013, aren't related. Relations between the two have become strained over the prime minister's goal of rapidly making peace with traditional enemy India and his determination to prosecute former army chief Pervez Musharraf for treason. Mr. Musharraf ended Mr. Sharif's previous stint as prime minister with a coup in 1999.