WASHINGTON — Secretary of State Mike Pompeo left open the possibility on Wednesday of entering a conflict with Iran without first seeking explicit congressional approval, telling senators “there is no doubt there is a connection” between Al Qaeda and Iran.

His comments came two days after the Trump administration designated Iran’s Islamic Revolutionary Guards Corps as a foreign terrorist group, and were likely to fuel concerns of American military action against the country.

Senator Rand Paul, Republican of Kentucky, pushed Mr. Pompeo to commit that the Trump administration would not attack Iran under a war authorization allowing the use of military force against Al Qaeda and other extremist groups responsible for the terrorist attacks of Sept. 11, 2001.

Mr. Pompeo demurred, saying he would “prefer to just leave that to lawyers.”

Mr. Paul, a libertarian who promotes isolationist policies, said he was troubled by Mr. Pompeo’s response. “I can tell you explicitly, you have not been given power or authority by Congress to have war with Iran,” he said in the exchange at a hearing of the Senate Foreign Relations Committee.