ANKARA, Turkey—Voters extended President Recep Tayyip Erdogan’s 15-year hold on power and endorsed his increasingly authoritarian model of government in one of Washington’s most important but often defiant NATO allies.

With 98% of ballots counted, Mr. Erdogan had secured 52.5% of the vote, which would eliminate the need for a runoff, state-run news agency Anadolu reported. His nearest opponent, Muharrem Ince, a lawmaker from the secular Republican People’s Party, garnered 30.8%.

Mr. Erdogan’s party and alliance partner garnered 53.6% of the vote in legislative elections, allowing the president to also maintain control of Parliament, Anadolu reported.

“The nation has given me the duty as president,” the 64-year-old Mr. Erdogan said in a victory speech from Istanbul. In Ankara, drivers honked their horns and supporters waved Turkish flags along the main boulevards of the capital. He had campaigned on his motto that “a great Turkey needs a strong leader.”

An unusually united opposition, however, said numbers released by Anadolu were manipulated, suggesting further tension and uncertainty in the strategic linchpin between the West and the Middle East.