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ALBANY — The closed-door meeting of the State Senate Democrats began with a discussion about social media use. But it quickly devolved into a shouting match, with two senators exchanging personal attacks before one stormed out of the room.

The confrontation on Wednesday, confirmed by three people who witnessed the exchange, is the latest sign of the growing rift between the party’s established core and its newly empowered progressive wing.

The clash occurred between Senator Kevin Parker of Brooklyn, who is in his ninth term, and Senator Alessandra Biaggi, who won a seat in the Bronx last year by dethroning Jeffrey D. Klein, a powerful Democratic incumbent, in the primary.

The skirmish highlighted the shifting dynamics in Albany, where Democrats have simultaneously cheered the new energy and reform spirit, and been leery of pushing it too far. A similar battle in Washington has captured national attention, as the Democratic leadership in Congress has sought to contain the outsider streak of new members like Representative Alexandria Ocasio-Cortez.