WASHINGTON — Six days after Democrats swept to power in the House, a quartet of newly elected women of color met in Washington for the first time. Somebody snapped a picture, and one of them — Alexandria Ocasio-Cortez — posted it on Instagram with a one-word caption: “Squad.”

Today, that foursome — Representatives Ocasio-Cortez of New York, Ayanna S. Pressley of Massachusetts, Ilhan Omar of Minnesota and Rashida Tlaib of Michigan — may be Washington’s best-known political clique. But their forceful brand of progressive politics and command of the spotlight rankles some fellow Democrats, including the most important Democrat in Washington: Speaker Nancy Pelosi, who on Friday appeared to make peace with Ms. Ocasio-Cortez — at least for now.

“In a family, you have your differences, but you’re still family,” Ms. Pelosi told reporters after the two met privately for 30 minutes, at Ms. Ocasio-Cortez’s request. She acknowledged “some personality issues” in the caucus, but called them “minor.”

Lionized by the liberal left and vilified by President Trump — who is waging a relentless campaign to attack them as anti-American — Ms. Ocasio-Cortez and the others roared into Washington in January as part of the most diverse freshman class in American history, and quickly emerged as a proxy for the debate over the future of the Democratic Party, exposing its ideological and generational divisions.