Just on Friday, the group announced an additional $17 million digital ad buy.

The partnership between American Bridge and Unite the Country represents an attempt to present themselves as this campaign’s leading outside Democratic entity — and to pre-emptively box out Priorities from making that claim.

Allies of both Bridge and Priorities have been pressing Democratic officials to nudge Mr. Biden’s campaign to send a signal about which group it prefers, according to people directly familiar with the conversations.

Yet it’s unclear how Mr. Biden’s campaign views the matter and whether it will signal such a preference. His team is somewhat restricted because campaign finance laws prohibit overt coordination between campaigns and super PACs.

And on Monday, a representative for Mr. Biden declined to say which, if any, of the groups the campaign wanted to see as the main outside organization.

During the primaries, Unite the Country had been the lone major super PAC supporting Mr. Biden.

But after Mr. Biden scored major victories on March 10, top officials at both Priorities and American Bridge — within minutes of each other — tweeted their support for Mr. Biden, declaring him to be the de facto nominee.

“We will be ALL IN to elect @JoeBiden as our next President,” wrote Mr. Beychok, the American Bridge president.

“The math is now clear,” said Guy Cecil, the chairman of Priorities. “Joe Biden is going to be the Democratic nominee.”