President Barack Obama's request for congressional permission to wage war against the Islamic State group doesn't go far enough to defeat the jihadist fighters, the US legislature's top Republican said Sunday.

Tantamount to a declaration of war, the authority sought from Congress last week would provide Obama political cover at home and a firmer legal basis on which to prosecute the fight.

The US military has already been involved in airstrikes against Islamic State in Iraq and Syria since the middle of last year, and Obama on Wednesday asked Congress to formally back a global war against the group -- but with limitations on the authorization's duration and curbs on the use of ground forces.

House Speaker John Boehner, however, was sharply critical of the request, which he described as less than "smart."

"The president is asking for less authority than he has today under previous authorizations. I don't think that's smart," said Boehner, the top Republican in the House of Representatives.

"We need a robust strategy to take on ISIL (IS). No one has seen one from this White House yet. In addition to a robust strategy, I think we need to have a robust authorization," he said.

"I don't believe what the president sent here gives him the flexibility, or the authority, to take on this enemy and to win," Boehner told the Fox News Sunday program.

"I look at the submission by the president as the beginning of the process," he added promising an "exhaustive series of congressional hearings.

"There will be a lot more discussion about this in the weeks ahead."