LONDON—Rishi Sunak, a former hedge-fund manager and U.K. Treasury chief, formally became Britain’s prime minister on Tuesday after he was appointed by King Charles III, vowing to steer the U.K. through a period of growing political and economic troubles.

In his first speech as prime minister, Mr. Sunak warned of a “profound economic crisis” facing the country, which is suffering from stagflation and has recently plunged into deeper political uncertainty with three different prime ministers in seven weeks.

Mr. Sunak said he would keep the current chancellor of the Exchequer, Jeremy Hunt, who stepped in to undo Ms. Truss’s tax-cut plan and regain market confidence.

Britain’s first Hindu leader pledged to repair the damage caused by the ill-fated experiment in British Reaganomics of his predecessor, Liz Truss, who was forced from office after markets were spooked by large unfunded tax cuts and a generous subsidy for household energy costs.

“Some mistakes were made. Not born of ill will or bad intentions. Quite the opposite in fact, but mistakes nonetheless. And I have been elected as leader of my party and your prime minister, in part to fix them,” said Mr. Sunak, as he stood in front of Downing Street. “I will place economic stability and confidence at the heart of this government’s agenda.”

“I will unite our country not with words, but with action,” Mr. Sunak said. “I will work day in and day out to deliver for you.”

President Biden spoke Tuesday with Mr. Sunak to congratulate him on his appointment as prime minister, according to a U.K. government readout. The two men discussed bilateral cooperation, including efforts to counter China’s “malign influence,” as well as efforts to bolster Ukraine in its war against Russia.

King Charles III welcomed Britain's new prime minister, Rishi Sunak, at Buckingham Palace on Tuesday.