LONDON — Leo Varadkar took office Wednesday as Ireland’s youngest Taoiseach, or prime minister. The son of an Indian immigrant, he is the first openly gay politician to serve in that post.

“I’ve been elected to lead but I promise to serve,” the 38-year-old said.

Varadkar, a doctor who has held three previous Cabinet posts, defeated rival Simon Coveney in a contest to replace Enda Kenny, who resigned.

Coveney won the votes of a majority of party members, but Varadkar was backed by most lawmakers and local representatives to give him victory under the center-right Fine Gael party’s electoral college system.

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