Washington must take a leading role. The U.S. has great resources and coalition-convening power, but it lacks influence with the various forces of the opposition and has limited knowledge of the elements in Syria that can best shape a post-Assad government. Democratic Turkey’s help on this front will be paramount.

Mr. Erdogan once made close ties to Assad a pillar of Turkey’s foreign policy. He reversed course months after the anti-Assad uprising began over two years ago and threw his support behind the opposition. He is anxious to see a return of stability in Syria, and the return of some 400,000 Syrian refugees who have fled to Turkey. This could ease the prime minister’s serious domestic financial and political problems before his planned revision of the constitution this year to allow for the more powerful presidency he aspires to.

However important a more stable and democratic-leaning Syria is to the U.S. and Turkey, their visions of how to achieve that objective may diverge. The major concern for Washington is that Turkey–now led by an avowedly secular but Islamic-oriented government–is pursuing a sectarian religious agenda in Syria, particularly through political and military support for the Muslim Brotherhood and allied rebels.

Throughout the Middle East, Turkey has sought close relations with Sunni Islamist governments in Egypt, Tunisia and Gaza. This pattern and Syria’s terrible disorder suggest that the Turkish government will favor quickly establishing a post-Assad government dominated by Syria’s Sunni majority, paying little attention to the needs of Syria’s minorities, some of whom have strongly supported Assad.

Mr. Erdogan’s preference for Sunni domination could be reinforced by concern about the political future of Syria’s Kurds. In recent months he has taken impressive, significant steps to end a three-decades-long guerrilla conflict with the Kurdistan Workers’ Party, or PKK, a nationalist movement with a strong presence among Syria’s Kurds. Whether this effort will succeed is not clear, and timing is crucial. Mr. Erdogan will be wary of accepting a post-Assad Syria–with its possibly restive and autonomy-seeking Kurds–unless Ankara has sufficient control over its own Kurdish regions.

From the U.S. perspective, however, the political participation of minorities–especially the Kurds, but also Alawites, Druze and Christians–will be important in determining the stability of post-Assad Syria. Sunnis, making up three-quarters of Syria’s population and long oppressed by the predominantly Alawite Assad regime, will have a leading role in any new Syrian government.

Yet if the Muslim Brotherhood or some other Sunni regime asserts the tyranny of the majority without protecting minority interests, civil strife and refugee flows could well continue. Worse, if such a government is dominated or influenced by al Qaeda-allied extremists, post-Assad Syria could become a breeding ground for global terrorism.

There is urgency if the U.S. is to try to create a reasonably stable, more pluralist Syrian government. Equally important will be pressing Turkey to support that effort as an indispensable ally. Both leaders could begin by designating high-level officials to address the challenges of a post-Assad Syria–although Mr. Erdogan will be less inclined to cooperate if Mr. Obama offers little American involvement in bringing Assad down.