WASHINGTON — With pressure building here for America to engage Syria and Iran in a last-ditch effort to stabilize Iraq, the pieces may be falling into place for a rapprochement between Washington and Damascus.

Yesterday, America’s closest ally, Britain, sent an envoy to Damascus for talks with President Assad and Foreign Minister Walid al-Moallem in the highest-level British diplomatic visit to the Syrian capital in years. Also yesterday, the Associated Press reported that Mr. Moallem was considering a visit to Baghdad, the Syrian foreign minister’s first diplomatic trip to post-Saddam Hussein Iraq and a de facto recognition of the new government’s legitimacy.

Cooperation with the democratically elected government in Baghdad, along with an end to support for the insurgency trying to sabotage it, are the two paramount demands the Bush administration has placed on Mr. Assad since the fall of Saddam.

The diplomatic maneuvers come as momentum appears to be increasing for a radical change of course on Iraq policy. The congressionally appointed Iraq Study Group, headed by a Bush family confidant and former secretary of state, James Baker, is likely to recommend renewed engagement with Iraq’s neighbors. Leading Republicans such as the chairman of the Senate Armed Services Committee, John Warner of Virginia, have already said they are looking forward to the Iraq group’s recommendations, which are on course to be released in January.

Iraq’s neighbors, particularly Iran and Syria, have played an active role in harboring, funding, and arming the Shiite and Sunni terrorists and militias that are killing Iraqi civilians. In the last five weeks, Iraq’s president and premier have said bluntly that “meddling” from the country’s neighbors must stop.

When asked yesterday about the Damascus visit by a foreign policy adviser to Prime Minister Blair, Nigel Scheinwald, a State Department official said, “If the British reported that there was some new movement by the Syrians in regard to our long-standing requests for them to change their behavior, we would look closely at that.”

As for the likely Iraq visit by Syria’s foreign minister, the official, who requested anonymity, said America would “welcome positive engagement by the Syrians in support of the legitimate Iraqi government.”

Nonetheless, America’s list of concerns about Syria is long. It includes Syria’s policy of helping funnel arms to the terrorist group Hezbollah in southern Lebanon before, during, and after this summer’s Hezbollah-Israel war; the support Syria provides to terrorists who attack Americans and Iraqis; and Syria’s insistence on hosting terrorist organizations operating against Israel.

A Syria expert at the Washington Institute for Near Easy Policy, Seth Wikas, said yesterday that Mr. Moallem’s possible visit to Baghdad was motivated by the refugees that have flooded into Syria since 2003. “This has more to do with the fact that Iraqis are coming into Syria like nobody’s business and this is putting strain on the Syrian economy. If you go to the Interior Ministry in Damascus and see the passports the clerks are processing, 75% are Iraqi. There are certain neighborhoods in Damascus that have become Iraqi. The no. 1 issue on the Syrian-Iraqi joint agenda is how to deal with the flow of Iraqis coming into the country,” Mr. Wikas said.

Mr. Wikas estimated that between 450,000 and 500,000 Iraqi refugees now live in Syria, with 250,000 in Damascus alone.

Another Syria expert at the Foundation for the Defense of Democracies, Tony Badran, said he did not see the recent diplomatic movements as evidence of a thaw in American-Syrian relations. He pointed to a meeting last week between the Syrian opposition group known as the National Salvation Front and members of the National Security Council, as well as recent statements by Secretary of State Rice criticizing Syria’s arms shipments to Hezbollah.

“If you monitor Syrian media, they spin the most irrelevant of visits and statements, even from former Soviet officials, into victories. It’s more a propaganda war than anything else.” Mr. Badran said.