(CNN) -- Iran continues to "interfere" in Iraq, including training insurgents and paying surrogates, the U.S. commander in Iraq told CNN on Sunday.

But Army Gen. Ray Odierno said his mission is limited to providing security within Iraq, no matter the provocation from Iran or elsewhere.

"I'm not authorized to do anything outside the borders of Iraq," he said on the CNN program "State of the Union."

Iran's government has repeatedly denied fomenting violence inside Iraq.

Despite some high-profile bombings and attacks in recent days, Iraq's security forces are ready to take over for U.S. forces this week to stabilize the nation's major cities, Odierno said.

He said he's seen a "constant improvement" in both the security situation and governance in Iraq to prepare for the June 30 deadline for U.S. troops to withdraw from major cities.

"They've been working for this for a long time," Odierno said.

The shift is part of the security agreement that former President George W. Bush's administration signed with Iraq.

Odierno said the situation has improved, despite the recent violence he blamed on "extremist elements using the timeframe and date to gain attention to themselves and divert attention from the success of Iraqi security forces."

The 131,000 U.S. troops in Iraq still will "maintain full coordination with Iraqi forces inside the cities" and continue to have intelligence capacity, Odierno said. With approval from the Iraqis, they also will carry out operations in major cities as necessary, he said.

Odierno said his goal is to help provide security that allows Iraq to hold planned national elections leading to the eventual removal of all U.S. troops by the end of 2011.

He said his biggest worry is a breakdown in stability such as a "consistent increase in violence" or a situation that Iraqi forces can't handle.

"I don't see that" happening, Odierno said. "I think we're on the right path."