Untraceable cash flows into super PACs supporting both presidential candidates.

As Democrats built toward their nomination of Joseph R. Biden Jr. and President Trump called into Sean Hannity’s show on Fox News, federal election regulators released the latest fund-raising figures in the race on Thursday night.

America First Action, a leading super PAC supporting President Trump’s re-election, took in $13.4 million last month, those filings showed. Roughly three-quarters of that came through the group’s dark-money sister nonprofit, making the origins of the cash untraceable.

The biggest gift with a name attached to it — a $2 million one — came to the group from Patricia J. Duggan of Florida, a prominent Scientologist who has poured hundreds of millions into the church.

A super PAC supporting Mr. Biden, Priorities USA Action, reported taking in $6.9 million in July, with roughly 40 percent of that coming from its comparable dark-money arm that does not disclose donors.