A woman walks along a street past graffiti that reads "Victory coming" in Deir al-Zor, on April 20, 2013. (Reuters)

When President Obama welcomes the leader of Qatar to the White House on Tuesday, he will doubtless thank the Qataris for hosting a major U.S. air base in the Persian Gulf, and for their help on a wide range of strategic issues from Libya to Afghanistan.

But he is also likely to press Emir Hamad bin Khalifa al-Thani to ensure that none of the weapons Qatar is sending to Syrian rebels end up with the Jabhat al-Nusra, which the administration has linked to al-Qaeda, and other Islamic extremist groups fighting against the government of Syrian President Bashar al-Assad.

Allegations that some Qatari aid is flowing to extremists have been made primarily made by Qatar’s Persian Gulf neighbors, which are rivals for regional influence and which have their own equities in the outcome in Syria. All are friends of the United States, and their rivalry has put the Obama administration in a difficult position as it tries to establish the parameters of its Syria policy.

Until recently, the administration exhorted its friends in the region not to send any weapons to Syria, lest they increase the bloodshed there. But as the civil war has dragged on for two years — and Assad has shown no signs of leaving — the United States has slowly stepped up its assistance to include non-lethal military support, while acknowledging and tacitly welcoming arms that are being supplied by both Saudi Arabia and Qatar.

Controlling the destination of those weapons, however, has proved problematic. At a meeting last weekend in Istanbul with opposition political and military leaders, all 11 governments in the self-styled “core group” of rebel backers agreed to channel military assistance only through the umbrella Syrian Military Council command led by Gen. Salim Idris. The command promised it would provide the aid only to “approved” fighting groups.

Interactive Grid: Keeping track of the conflict in Syria through videos, images and tweets.

“Each country made a commitment to direct their military aid and assistance uniquely and solely to the military command,” Secretary of State John F. Kerry said at the close of the meeting.

“It’s one of the most important things that can make a difference to the situation on the ground,” Kerry said. In addition to the United States, the Saudis and Qatar, the core group includes Britain, Egypt, France, Germany, Italy, Jordan, Turkey and the United Arab Emirates.

The question now is whether the agreement will stick, and whether Obama can help keep the core group on the same page. Earlier this month, he met in Washington with United Arab Emirates Crown Prince Mohammed bin Zayed Al Nahyan and, separately, with Saudi Arabian Foreign Minister Saud al-Faisal.

In the next few weeks, Obama will also host Jordanian King Abdullah and Turkish Prime Minister Recep Tayyip Erdogan, whose countries share a border with Syria and have accepted hundreds of thousands of Syrian refugees.

All countries in the region fear an explosion of instability as the war increasingly takes on sectarian coloration. Most of the rebels are Sunnis, part of the Syrian majority that has long been oppressed by Assad’s minority Alawites, a Shiite sect. Other minority groups, including Christians and Druze, have been reluctant to abandon Assad as Islamic extremists — with at least rhetorical backing from al-Qaeda — have taken a more prominent role within the opposition military force.

In some rebel areas under extremist control, Islamists have imposed social restrictions including banning smoking, drinking and uncovered women.

The fractured political opposition has been unable to convince minority Syrians — and even some in their own camp — that they are committed to a pluralistic government to replace Assad, and are capable of keeping the country in one piece. Within the rebel military ranks, support has tended to gravitate to those who are the most capable, better-equipped fighters — often the extremists.

Not all weapons and money to buy them are coming from Persian Gulf governments, U.S. officials said. Individuals in gulf countries who would favor a more religious coloration in Syria are also contributing.

A senior State Department official at the Istanbul meeting, who spoke on the condition of anonymity about the vexing Syrian problem, related a recent conversation he said he had with a senior commander of the Syrian Military Council.

“He said, ‘Some of my men, through their own connections, family and friends, know people in the gulf, business people who can literally get them millions of dollars in cases within a few days,’ ” the official recounted. He summarized the commander’s dilemma: “How do I tell my guys, Don’t take that money from that business guy who is backed by an Islamist network?”

Kerry and other U.S. officials described the Istanbul meeting as a turning point, at which the opposition political leadership promised to rededicate itself to seeking a political solution to the war, albeit without Assad as a negotiating partner — along with unity of purpose and protection of minority rights.

Away from the Syrians, donor countries argued for hours behind closed doors about their own disputes.

“How can we make those asks of the [opposition] coalition when we know we actually have to sort out our own house?” said another diplomat at the Istanbul meeting.