David Petraeus, the retired Army general and former CIA director, apologized Wednesday before the Senate Armed Services Committee for his high-profile extramarital affair, and then proceeded to lay out his his vision for how the United States should handle the ongoing conflict in Iraq and Syria.

Petraeus, appearing before a congressional committee for the first time since resigning as CIA director in November 2012, said that he thought it would be “appropriate to begin my remarks this morning with an apology.” He stepped down after his affair with his biographer, reserve Army officer Paula Broadwell, came to light, and pleaded guilty in April to mishandling classified information and providing it to her.

“Four years ago, I made a serious mistake, one that brought discredit on me and pain … to those closest to me. It was a violation of the trust placed in me and a breach of the values to which I’d been committed throughout my life,” Petraeus said, reading from a statement on a table in front of him.

“There’s nothing I can do to undo what I did. I can only say, again, how sorry I am to let — to those I let down and then strive to go forward with a greater sense of humility and purpose and with gratitude to those who stood with me during a very difficult chapter in my life,” he added.

Petraeus said “it means a great deal” that the committee’s leaders asked him to share his views on the Middle East. The region, he said, does not play “by Las Vegas rules. What happens in the Middle East is not going to stay in the Middle East.”

The retired general said that the military coalition assembled to fight the Islamic State militant group is impressive, and that “some elements of the right strategy are in place.” But others are under-resourced or missing, and the effort overall is not where it should be at this point, he added.

“In my judgment, increased support for the Iraqi security forces, Sunni tribal forces and Kurdish Peshmerga is needed, including embedding U.S. adviser elements down to the brigade headquarters level of those Iraqi forces fighting ISIS,” Petraeus said, using one of the acronyms for the militant group. “I also believe that we should explore use of joint tactical air controllers with select Iraqi units to coordinate coalition airstrikes for those units.”

Petraeus said the United States also should examine whether its rules of engagement on precision airstrikes are too restrictive, but added that the U.S. military should exercise restraint to make sure it does not “take over” Iraqi units.

“I would, not, for example, embed U.S. personnel at the Iraqi battalion level nor would I support clearance operations before a viable hold force is available,” he said.

Petraeus said the the center of gravity in defeating the militants lies in Baghdad and Iraq’s central government. Washington doesn’t have the proper organization in place to support that, though, he added. He advocated moving a part of the U.S. military’s operational headquarters from Iraq to Baghdad, saying U.S. Ambassador Stuart E. Jones doesn’t “always have a day-to-day military counterpart.”

The U.S. military headquarters in Baghdad would focus primarily on operations in Iraq, while another commanding officer could be placed in Turkey or another location to oversee operations in Syria, Petraeus said. He called the country a “geopolitical Chernobyl, spewing instability and extremism over the region and the rest of the world.”

The problems in Syria cannot quickly be resolved, but the United States can take actions that will make a difference, the retired general said.

“We could, for example, tell Assad that the use of barrel bombs must end. And that if they continue, we will stop the Syrian Air Force from flying,” he said. “We have that capability.”

Petraeus was greeted by senators warmly. Sen. John McCain (R.-Ariz.), chairman of the committee, called him “one of our most distinguished leaders.” Sen. Jack Reed (D.-R.I.) thanked him for his “very incisive and extraordinarily erudite treatment of these complex issues.”