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Vice President Joseph R. Biden Jr. on Saturday summoned Senator Elizabeth Warren, Democrat of Massachusetts, to his Washington residence for a meeting, the latest indication that he is seriously considering a presidential bid.

Mr. Biden and Ms. Warren met for lunch on the veranda at the Naval Observatory with no aides present, according to a Democrat briefed on the conversation.

The conversation, which lasted for well over an hour, touched on policy issues and both the Republican and Democratic presidential primary campaigns. Mr. Biden made clear that he was seriously considering a bid of his own, but did not directly ask Ms. Warren for her support.

The discussion about what has been an unpredictable presidential campaign — in which Senator Bernie Sanders of Vermont has shown strength on the left and Donald J. Trump has emerged as a force on the right — centered on “what the country is trying to tell us,” said the Democrat briefed on the lunch.

Mrs. Warren was the dream presidential candidate of many progressives and still retains a loyal following among liberal activists.

The meeting comes as Mr. Biden — whose eldest son, Beau, died in May — has begun to intensively test the waters for a third White House run, meeting with his small inner circle and telephoning Democratic donors.

The meeting Saturday, first reported by CNN, came at Mr. Biden’s request this week.

An aide to Mr. Biden said only that he returned at the “last minute” to Washington and then planned to travel back to his home state of Delaware, where he has gathered with relatives and advisers over the last week.

Ms. Warren has helped set the agenda for progressive policy in her brief time in the Senate, and has become a favorite of the left for her fiery rhetoric against financial institutions.

She told WBZ-TV, a Boston station, on Friday that no one “has been anointed” for the Democratic nomination.

Ms. Warren met near the end of last year with Hillary Rodham Clinton, the leading candidate in the polls for the Democratic nomination. But Ms. Warren and Mrs. Clinton are not natural allies, and they have had a sometimes tense relationship over the years.

Mrs. Clinton has also seen her personal favorability ratings dip amid questions about her use of a private email server during her time at the State Department, and Mr. Biden’s allies are watching to see what happens with that issue as he weighs his decision, which may not come until well into September.