When the Americans had participated in previous rounds of talks in Geneva, the meetings took place at the Palace of Nations, one of the stolid lakeside edifices built in the first half of the 20th century that have housed the United Nations since it was formed after World War II. Those buildings symbolized a postwar order that tried to institutionalize human rights and the laws of war, an order associated with American leadership — or domination — amid the tensions of the Cold War.

Now, the role of the United States in Syria and across the Middle East is widely seen as having receded under former President Barack Obama, and its future remains uncertain. Mr. Obama, while backing some rebel groups, resisted deeper American involvement in the Syrian conflict, ceding the leading role to Russia. His successor, President Trump, has signaled broad approval of Russian leadership and policies and sent mixed messages on Syria.

Officially, all sides in the Syrian conflict describe the goal of the talks in Astana as reaffirming a tenuous cease-fire in order to revive the Geneva talks. The cease-fire, started in December and known formally as a cessation of hostilities, is largely ignored in many parts of the country and excludes jihadist groups, including the Levant Conquest Front and the Islamic State.

A strengthening of the cessation across Syria, the United Nations envoy Staffan de Mistura said Monday, could pave the way for discussion of more substantive political issues at talks scheduled for February in Geneva. The United Nations initially resisted anything more than an observer role in the talks in Astana, but Mr. de Mistura at the last minute agreed to act as a mediator and was shuttling between the delegations who were in separate rooms.

Western diplomats were also watching warily to see whether the talks in Astana could be a Russian effort to ultimately replace the Geneva discussions, which the Russian government has criticized. The Syrian government and the Russians have long argued that the Geneva framework, calling for a transitional body with full governing powers, does not require President Bashar al-Assad to step down, while the opposition has insisted that it does.

But as a practical matter, an increasing number of Western countries, including the United States, and even some of the rebels’ backers in the Middle East, like Turkey, have moved toward the Russian position.

With Turkey mainly concerned about checking Kurdish militants within its borders and in Syria, and the United States focused on battling Islamic State militants, they have stopped pushing loudly for Mr. Assad to step down ahead of a settlement, instead signaling that they could accept some role for him in a transitional political arrangement.