But the United States, Iran, and Syria still very much differ on the ultimate goal of their talks.
The Baghdad security conference brought together these three key powers, who confront each other in Iraq.
But to judge by the initial public statements, all three consider their talks worthwhile.
"The meeting focused on how to help Iraq deal with the problems that emanate from the neighborhood, and also facilitate reconciliation in Iraq," U.S. Ambassador to Iraq Zalmay Khalilzad told U.S. television on March 11. "The exchanges were good. There was agreement that there will be working groups formed, involving Iraq and its neighbors to deal with security, to deal with the issue of oil and electricity, and also with the refugees."
"We support any efforts that will bring Iraq out of its current problems and we support any plan that is for Iraq's people and its government interests and that would help Iraq's security," Iranian Foreign Ministry spokesman Mohammad Ali Hosseini said on March 11.
Perhaps most importantly, the 16 delegations that took part in the ambassador-level talks also agreed to prepare for an expanded, follow-up conference -- likely at the ministerial level.
That conference, whose venue and time have yet to be determined, would again bring together representatives of United States, Iran, Syria, Turkey, the other permanent members of the UN Security Council, and several other states and regional organizations.
But it could also include other G8 members to give the proceedings further weight.
Tehran -- like Washington -- is calling all these prospects positive.
"We support any efforts that will bring Iraq out of its current problems and we support any plan that is for Iraq's people and its government interests and that would help Iraq's security," Iranian Foreign Ministry spokesman Mohammad Ali Hosseini said on March 11. "Iran will be the first supporter of any such plan."
Syria, too, is welcoming the process. State-controlled newspapers on March 11 said Damascus supports "a political solution" to end the violence in Iraq.
But even as all sides put a positive assessment on this first of-its-kind meeting in Baghdad, they also are underlining how much they differ on the final goals for their talks.
U.S. President George W. Bush said he wants to see Iran and Syria stop actions Washington says contribute to attacks on coalition forces and to Iraq's sectarian conflict.
Bush said on March 11 that "there are things for them to do, such as cutting off weapons flows and/or the flow of suicide bombers into Iraq."
The U.S. president was speaking while on a state visit to Colombia.
Iran said it wants to see the United States change its Iraq policy and turn responsibility for Iraq over to the Iraqis.
That is language often used by Tehran in combination with demands Washington set a timetable for withdrawing from Iraq.
An Iraqi soldier provides security for the March 10 conference in Baghdad (epa)"We hope that other countries present at the Baghdad conference will change their political behavior toward Iraq, and also the Baghdad conference emphasized that the countries which are involved in Iraq should give responsibilities to Iraq's people and government," Iranian Foreign Ministry spokesman Hosseini said.
Iran is a major backer of Iraq's Shi'ite political groups, which dominate the Baghdad government. Washington accuses Tehran of also providing military expertise and technology to Iraqi Shi'ite militias.
Iran And Syria
Many analysts say Tehran would ultimately like to see the talks that begin over Iraq end in much broader discussions with the United States and other world powers over Iran’s controversial nuclear program.
If so, that would put Tehran in a position to offer cooperation in Iraq in exchange for eased international pressure to end its own uranium-enrichment program.
Washington has consistently ruled out talking with Iran about anything other than Iraq.
U.S. and other Western officials have conditioned any talks on the nuclear crisis to Iran first stopping uranium enrichment and other activities that could help developing nuclear weapons.
As for Syria, many observers believe Damascus also wants the Baghdad meeting to lead to more than just talks about Iraq.
The United States charges Syria with doing too little to stop the flow of money and foreign fighters to Iraq's Sunni insurgent groups.
But Syrian officials might ultimately hope to trade cooperation on Iraq for concessions to Damascus elsewhere in the region.
One hoped-for concession might be for the West to ease its efforts to keep Damascus from influencing events in Lebanon, where the Syrian officials have high political and financial interests.
Another hoped-for trade-off for Syria might include getting U.S. support for renewed talks over the Golan Heights. That is land Israel captured from Syria in 1967 and later annexed, but which Damascus wants back.
Still, for now, all participants in the March 10 conference at least share the immediate goal of continuing talking about Iraq.
And they have charged the Iraqi government with the difficult process of finding a place and time agreeable to all.
But even there, there are differences.
The Iraqi and Iranian governments are reported to favor holding a meeting in Baghdad again. The United States is said to want Istanbul. And the Egyptian government has offered Cairo.
Whatever the venue, the meeting is expected to be held as soon as next month.