But ambassador Zalmay Khalilzad on Monday refused to specify what consequences Damascus might face.
His tough talk on Syria is part of a US pressure campaign in many foreign capitals and at the United Nations gathering this week in New York.
"Our patience is running out, the patience of Iraqis are running out. The time for decision ... has arrived for Damascus," Khalilzad said.
Speaking to reporters at the US State Department, Khalilzad refused to rule out either a military strike on Syria or an attempt to further punish Syria through the United Nations
"All options are on the table," he said.
The United States says the Baathist government in Syria allows a free flow of foreign terrorists across its border with Iraq and turns a blind eye to terrorist training camps on its soil.
Khalilzad said young, would-be terrorists are flying openly to Syria, landing unmolested at the Damascus airport on one-way tickets.
"It simply is not tolerable that they, with impunity, can allow terrorists to come from other countries in the region, get training or pass through," to next-door Iraq, Khalilzad said.
"Syria has to decide what price it's willing to pay in making Iraq success difficult. And time is running out for Damascus to decide on this issue"
US ambassador to Iraq
"It simply must close the training camps," he said. "It should not allow youngsters misguided by al-Qaida, from Saudi Arabia, from Yemen, from North Africa, to fly into Damascus international airport.
"It shouldn't be that hard, if you see young men between the ages of 18 and 28, who are coming without a return ticket, landing in Damascus airport, to control that."
No proof offered
The ambassador is in Washington to accompany Iraqi President Jalal Talabani as he visits the White House and meets with members of Congress.
Khalilzad offered no proof of claims of Syrian interference, which he called "blatant", and gave no specifics about US options to counter Syria.
Khalilzad (L) is in the US with
Iraqi President Jalal Talabani (R)
"I would not like to elaborate more, they should understand what I mean," he said.
The US believes Iraqi Sunnis are refusing to agree a proposed constitution because of threats from Sunni fighters who have infiltrated Iraq from Syria, where they have training camps, Khalilzad said.
"Syria has to decide what price it's willing to pay in making Iraq success difficult. And time is running out for Damascus to decide on this issue," the ambassador warned.
An official Syrian source said Iraqi officials were fully aware that Damascus was doing whatever it could to control the border on its side.
The source blasted statements out of Baghdad blaming Syria for the chaos in Iraq, saying they were aimed at covering up the failure to achieve peace in Iraq.
Source: Aljazeera + Agencies