The newly elected No. 2 Republican in the U.S. House of Representatives said on Sunday he would not rule out sending American troops to Iraq to help Baghdad in its fight against a Sunni insurgency.

Representative Kevin McCarthy, who was elected last week to the majority leader's post in the House, also said President Barack Obama needed to lay out an overall strategy for dealing with terrorism in the Middle East region.

Asked on "Fox News Sunday" whether he would support putting "boots on the ground" in Iraq, McCarthy said: "I'd put everything on the table. But most people, when you talk to them, don't think boots on the ground work right now."

Obama announced last week he was sending up to 300 military advisers to Iraq's Shi'ite-led government, which is fighting an insurgency led by the Sunni militant group Islamic State of Iraq and the Levant (ISIL).

Obama, who withdrew U.S. troops from Iraq at the end of 2011, has ruled out sending troops back there and has urged the Baghdad government to take urgent steps to heal the country's sectarian rift.

McCarthy said he supported Obama's decision to send the advisers, which will staff joint operations centers for intelligence sharing and planning, but he also called on Obama to outline a broader strategy for combating terrorism.

"I do not have a problem with sending the 300," McCarthy said. "What are they going to do? If you don't have an overall strategy, how do we push back this momentum of this terrorism that is growing throughout the entire region."

McCarthy was elected on Thursday to the majority leader's job by his fellow Republicans in the House, moving up from the No. 3 position. He takes over after the current majority leader, Eric Cantor, said he would step down on July 31 after losing to a Tea Party conservative this month in a primary election.

(Reporting by Eric Beech; Editing by Jim Loney and Gareth Jones)