Lawyers for House Democrats, the Justice Department and Mr. McGahn had tentatively struck a deal to provide the testimony earlier in May. But the scheduling was delayed for weeks while they waited to see what Mr. Trump, who was not a party to the agreement, would do. Mr. McGahn’s agreement to testify — with President Biden’s permission — was contingent upon there being no active legal challenge to his participation in the matter, according to the two people, who spoke on the condition of anonymity because of the legal and political sensitivity of the matter. Immediately after the deal was announced this month in a court filing, a lawyer for Mr. Trump had conveyed that the former president intended to intervene. Former presidents can invoke executive privilege, although courts weigh that against the view of the incumbent president, and Mr. Trump could have sought a court order blocking Mr. McGahn’s testimony.