Vice President Mike Pence telephoned Vice President-elect Kamala Harris Thursday to congratulate her and offer his assistance ahead of next week’s swearing-in, the latest indication that Mr. Pence is filling the leadership role all but abdicated by President Trump.

The conversation, which was relayed by two officials briefed on the call, was described as gracious and pleasant. The discussion is the first time Mr. Pence and Ms. Harris have spoken since they debated each other last fall.

It also represents the only one-on-one conversation between elected officials in the outgoing and incoming administration: Mr. Trump has refused to call President-elect Joseph R. Biden Jr. and has not even fully conceded defeat in his public remarks.