WASHINGTON  President Obama has issued signing statements claiming the authority to bypass dozens of provisions of bills enacted into law since he took office, provoking mounting criticism by lawmakers from both parties.

President George W. Bush, citing expansive theories about his constitutional powers, set off a national debate in 2006 over the propriety of signing statements  instructions to executive officials about how to interpret and put in place new laws  after he used them to assert that he could authorize officials to bypass laws like a torture ban and oversight provisions of the USA Patriot Act.

In the presidential campaign, Mr. Obama called Mr. Bush’s use of signing statements an “abuse,” and said he would issue them with greater restraint. The Obama administration says the signing statements the president has signed so far, challenging portions of five bills, have been based on mainstream interpretations of the Constitution and echo reservations routinely expressed by presidents of both parties.

Still, since taking office, Mr. Obama has relaxed his criteria for what kinds of signing statements are appropriate. And last month several leading Democrats  including Representatives Barney Frank of Massachusetts and David R. Obey of Wisconsin  sent a letterto Mr. Obama complaining about one of his signing statements.