Secretary of State Hillary Clinton greeted guests after President Barack Obama’s speech at Cairo University.

It’s hard to know whether to laugh or cry after reading the reactions of analysts and officials in the Middle East to President Obama’s Cairo speech. “It’s not what he says, but what he does,” many said. No, ladies and gentlemen of the Middle East, it is what he says and what you do and what we do. We must help, but we can’t want democracy or peace more than you do.

What should we be doing? The follow-up to the president’s speech will have to be led by Secretary of State Hillary Clinton. This will be her first big test, and, for me, there is no question as to where she should be putting all her energy: on the peace process.

No, not that peace process - not the one between Israelis and Palestinians. That one’s probably beyond diplomacy. No, I’m talking about the peace process that is much more strategically important - the one inside Iraq.

The most valuable thing that Mrs. Clinton could do right now is to lead a sustained effort - along with the U.N., the European Union and Iraq’s neighbors - to resolve the lingering disputes between Iraqi factions before we complete our withdrawal. (We’ll be out of Iraq’s cities by June 30 and the whole country by the close of 2011.)

Why? Because if Iraq unravels as we draw down, the Obama team will be blamed, and it will be a huge mess. By contrast, if a decent and stable political order can take hold in Iraq, it could have an extremely positive impact on the future of the Arab world and on America’s reputation.

I have never agreed with the argument that Iraq was the bad war, Afghanistan the good war and Pakistan the necessary war. Folks, they’re all one war with different fronts. It’s a war within the Arab- Muslim world between progressive and anti-modernist forces over how this faith community is going to adapt to modernity - modern education, consensual politics, the balance between religion and state and the rights of women. Any decent outcome in Iraq would bolster all the progressive forces by creating an example of something that does not exist in the Middle East today - an independent, democratizing Arab-Muslim state.

“The reason there are no successful Arab democracies today is because there is no successful Arab democracy today,” said Larry Diamond, a professor at Stanford University the author of “The Spirit of Democracy.” “When there is no model, it is hard for an idea to diffuse in a region.”

Rightly or wrongly, we stepped into the middle of this war of ideas in the Arab-Muslim world in 2003 when we decapitated the Iraqi regime, wiped away its authoritarian political structure and went about clumsily midwifing something that the modern Arab world has never seen before - a horizontal dialogue between the constituent communities of an Arab state. In Iraq’s case, that is primarily Sunnis, Shiites and Kurds.

Yes, in a region that has only known top-down monologues from kings, dictators and colonial powers, we have helped Iraqis convene the first horizontal dialogue to write their own social contract for how to share power.

At first, this dialogue took place primarily through violence. Liberated from Saddam’s iron fist, each Iraqi community tested its strength against the others, saying in effect: “Show me what you got, baby.” The violence was horrific and ultimately exhausting for all. So now we’ve entered a period of negotiations over how Iraq will be governed. But it’s unfinished and violence could easily return.

And that brings me to Secretary Clinton. I do not believe the argument that Iraqis will not allow us to help mediate their disputes - whether over Kirkuk, oil-sharing or federalism. For years now, our president, secretary of state and secretary of defense have flown into Iraq, met the leaders for a few hours and then flown away, not to return for months. We need a more serious, weighty effort. Hate the war, hate Bush, but don’t hate the idea of trying our best to finish this right.

This is important. Afghanistan is secondary. Baghdad is a great Arab and Muslim capital. Iraq has something no other Arab country has in abundance: water, oil and an educated population. It already has sprouted scores of newspapers and TV stations that operate freely. “Afghanistan will never have any impact outside of Afghanistan. Iraq can change minds,” said Mamoun Fandy, of the International Institute for Strategic Studies.

You demonstrate that Iraqi Shiites, Sunnis and Kurds can write their own social contract, and you will tell the whole Arab world that there is a model other than topdown monologues from iron-fisted dictators. You will expose the phony democracy in Iran, and you will leave a legacy for America that will help counter Abu Ghraib and torture.

Ultimately, which way Iraq goes will depend on whether its elites decide to use their freedom to loot their country or to rebuild it. That’s still unclear. But we still have a chance to push things there in the right direction, and a huge interest in doing so. Mrs. Clinton is a serious person; this is a serious job. I hope she does it.