The Ohio Republican told reporters Thursday that the United States continues to have vital interests in Iraq, from which Obama has withdrawn American combat troops.
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Boehner says U.S. progress in Iraq is clearly in jeopardy.
He says Obama's focus should be on completing the U.S. mission there and says the president should get engaged before it is too late. He says the U.S. should provide equipment and technical assistance to the beleaguered Iraqi government.
Meanwhile, Obama responded to Boehner's comments, saying the U.S. is prepared to take military action when its national security interests are threatened.
"I don't rule out anything" when it comes to helping Iraq deal with insurgents, said Obama.
Iraq Prime Minister Nouri al-Maliki has asked his parliament to declare a state of emergency that would give him increased powers, but the lawmakers have not done so.
Reports suggest Republicans on the Senate floor are also calling for a more aggressive military stance in Iraq.
Boehner is expected to remain in his position through this year and to seek re-election to the job in 2015 if Republicans maintain control of the chamber, as expected, in November.
He said that it is important for Republicans to quickly resolve the leadership issue.
But some conservative Republicans were speculating that whoever emerges as House Majority leader Eric Cantor's replacement could also become a challenger to Boehner for the speakership next year.
—By The Associated Press. CNBC contributed to this report.