WASHINGTON — As lawmakers grapple with President Obama’s claim that he already has congressional authorization for airstrikes against the Islamic State, legal specialists are saying that even legislative inaction could create a precedent leaving the executive branch with greater war-making powers.

Last week, the Obama administration asserted that a military campaign in Syria and Iraq against the Islamic State, also known as ISIS or ISIL, is covered by the existing 2001 authorization to use force against Al Qaeda and the 2002 approval of the Iraq War. But he said he needed new legislative authority for the related mission of providing military training for moderate rebels in Syria.

The House and Senate swiftly passed a rebel-training bill, but it did not address the executive branch’s claim about the 2001 and 2002 authorizations. Members of Congress have also introduced a flurry of bills that would explicitly authorize force against the Islamic State, but none repudiate the administration’s interpretation of existing laws, either.

The Obama legal team’s broad interpretation of the old authorizations has drawn criticism. But several legal specialists said that because Congress was on notice about how the executive branch was interpreting its 2001 and 2002 statutes, any failure to challenge that theory — especially as it enacted other legislation in connection with Islamic State policy — could be interpreted as ratifying it.