By Barbara Starr

The Pentagon is considering a proposal to train Iraqi forces in counterterrorism operations, a senior U.S. defense official tells CNN. It would be the U.S. military's most significant involvement with Iraq since U.S. troops withdrew from that country two years ago.

If the White House and the Iraqis approved the proposal, U.S. troops would not enter Iraq, but instead would train Iraqi forces in a third country, most likely Jordan, the official said. The idea had been considered and rejected by the Iraqis in the past. But the U.S. Central Command basically has dusted off the idea and is trying to see if it can gain traction in light of growing violence in Iraq, especially in Fallujah and Ramadi.

"Certainly in light of what we are seeing happening on the ground in Iraq, U.S. military leaders are pushing harder to begin that training," the official told CNN.

The idea is being discussed within the U.S. national security agencies and departments, and has not yet been approved by the President or offered to the Iraqis.

The U.S. military training would focus on training Iraqi forces to deal with al Qaeda or insurgent elements without unduly harming civilian populations, the official said.