The leaders of the committees said it was remotely possible that, if new evidence surfaced, the panels would resume public hearings in the fall.
The court will resume hearings on Friday, when the defendants will get a chance to comment on the charges against them.
This week, a House subcommittee is to resume hearings it has been holding on the blood supply.
The plan is now before the Supreme Court, which will resume hearings at the end of the month after a postponement.
A high-profile inquiry led by a senior judge, Lord Hutton, is to resume hearings on Monday into the suicide of the weapons expert David Kelly.
Congressional investigators have not yet decided whether to look into Mr. Casolaro's death when they resume hearings on the Inslaw case.
The nuns' testimony came as the Senate Governmental Affairs Committee, after a monthlong break, resumed hearings on campaign finance.
The House Banking Committee resumes hearings on troubled thrifts.
After a recess to avoid influencing the general election, the inquiry resumed public hearings on 29 June 2010.
The Legislation Committee will resume hearings early next year, Mr. Abinanti said.