As the primary season officially came to an end Tuesday night, Sen. Bernard Sanders met privately with Hillary Clinton — but the senator from Vermont senator still wasn’t ready to offer an endorsement to his presidential primary rival.

The campaigns described the 90-minute meeting as positive, though neither would release much detail. A statement from the Clinton camp said the two candidates discussed income inequality, debt-free college and other issues, and that they “agreed to continue working on their shared agenda, including through the platform development process for the upcoming Democratic National Convention.”

The Sanders campaign said afterward that the senator told Mrs. Clinton about the need to “bring more people into the political process,” suggesting that Mr. Sanders believes the Democratic Party should eliminate superdelegates, allow independents to vote in all party primaries and take other steps to increase access.

They met in Washington on the night Mrs. Clinton won the District of Columbia primary in a landslide. The victory, however, was of little consequence; the former secretary of state became the party’s presumptive nominee last week when she crossed the 2,383-delegate threshold to be approved on the first convention ballot.

Even after Mrs. Clinton hit that mark and the primary season, for all intents and purposes, came to an end, Mr. Sanders refused to officially concede and offer his endorsement. His perseverance has rattled Democrats on Capitol Hill and left some of his high-profile progressive supporters in a difficult position because virtually everyone in the party agrees it’s time to unite and begin plotting attacks against Republican candidate Donald Trump.

Mr. Sanders, who is scheduled to deliver a widely anticipated video address to his supporters Thursday night, seems set on going to the party convention in Philadelphia in July and using his leverage — including the nearly 1,900 delegates he won this primary season — to rewrite the Democratic platform in a more liberal fashion.

Mrs. Clinton was to deliver an address on national security Wednesday in Hampton, Virginia. Mr. Sanders had no events scheduled until his prime-time video speech.