The last time Iraqi Prime Minister Nouri al-Maliki visited the White House — in late 2011 — he and President Barack Obama touted Iraq’s political and security progress.

On Friday, al-Maliki arrived again, this time in search of help to fight a stunning resurgence of al-Qaida violence that has claimed 7,000 Iraqi deaths in 2013 — nearly 1,000 in October. It will be a hard sell.

Most Americans, including Obama, are eager to put the Iraq war out of mind. And as a bipartisan group of senators noted in a letter to Obama last week, al-Maliki’s “mismanagement” of Iraq’s sectarian politics has helped create the climate that permitted al-Qaida to re-emerge.

But Americans are fooling themselves if they think they can afford to ignore Iraq’s troubles. We and the Iraqis are still bound together in ways that few Americans realize.

For starters, Iraq’s al-Qaida problem is our problem, too.

Helped by the chaos in Syria, al-Qaida has sunk new roots in the adjacent areas of eastern Syria and western Iraq, where it trains thousands of foreign jihadis who can return home and cause havoc in Europe, Russia, and all over the Middle East.

“This new Islamic emirate stretches from the Mediterranean to the Gulf, from Turkey and the Caucasus to Jordan and Saudi Arabia,” says Michael Knights, an Iraq expert at the Washington Institute for Near East Policy. “It constitutes one continuous, borderless jihadi territory.”

Both the United States and Iraq contributed to the security decline over the last two years. Just as Syria began to fall apart, the United States withdrew all its troops from Iraq, after failing to reach an accord on leaving a small number behind. This hampered cooperation on intelligence sharing, counterterrorism, and protecting Iraq’s borders. Al-Qaida terrorists, who had been sheltering in Syria, were now free to move back to Iraq.

Of course, al-Maliki’s rebuff of Sunni demands for more power sharing in his Shiite-led government did help open the door to extremists. (His speech at the U.S. Institute of Peace on Thursday denying any culpability was not encouraging.) As we’ve seen in Syria, al-Qaida is masterful at manipulating sectarian politics among Arabs in order to gain a foothold. What gets insufficient attention is the role administration passivity played in accelerating Iraq’s downhill slide.

Prior to the troop withdrawal, intense U.S. efforts had helped mediate some dangerous disputes among Kurds, Shiites, and Sunnis. That mediating role is still needed. In April, Vice President Biden did help defuse a crisis between Maliki and Sunni opponents. But such efforts need to be more systematic to have an effect.

“We are hardwired into the Iraqi political system,” says Ryan Crocker, the former U.S. ambassador to Iraq, “because we helped create it.”

In a climate of fear, says Crocker, Shiites worry about a radical Sunni resurgence, and Sunnis fear eclipse. “Making compromises is seen as a sign of weakness. They can’t do these things by themselves,” he said.

It would take a very attentive U.S. administration to help smooth sectarian tensions. Yet, says Crocker, there has been only one secretary of state visit — by John Kerry — over the last five years. “We are not engaged,” he says, “and that engagement is absolutely necessary to get Iraqis to do the right thing or not do the wrong thing.”

What would such engagement look like?

Crocker thinks the administration should help the Iraqis strengthen their counterterror capabilities with better intelligence cooperation, military advisers, and, as the Iraqis are requesting, drones. For those who denounce drones, keep in mind that al-Qaida is blowing up schools, mosques, and markets filled with civilians in Iraq and Syria. If Iraq could hit al-Qaida targets inside Syria, that could save innumerable lives.

But Crocker says military aid alone is far from sufficient. He believes that more attention by Kerry — along with presidential phone calls — will be needed to steer al-Maliki and the Sunnis toward political accord, and to ensure fair Iraqi elections in 2014.

The strange thing is that Iraq could still become America’s strongest Arab ally. Iraq observers such as Knights believe the United States has more credibility among Iraqis than it realizes (although the relationship is fraught). Tied together by our painful past and by our common security threats, a focus on building a broad U.S.-Iraqi alliance is crucial. Finally.

“We now have an opportunity for an entirely new relationship with Iraq,” says Crocker. “We need to treat them as an ally, not leave them to their own devices.”

From his lips to Obama’s ears.