Jordan has also been touched by the fighting. Recent skirmishes have broken out between the Syrian military and Jordanians guarding the country’s northern border, where many families have ties to Syria. In August, a 4-year-old girl in a Jordanian border town was injured when a Syrian shell struck her house, and there are concerns in Jordan that a sharp upsurge in the fighting in Syria might lead to an even greater influx of refugees.

Jordan, which was one of the first Arab countries to call for Mr. Assad’s resignation, has become increasingly concerned that Islamic militants coming to join the fight in Syria could cross the porous border between the two countries.

The American mission in Jordan quietly began this summer. In May, the United States organized a major training exercise, which was dubbed Eager Lion. About 12,000 troops from 19 countries, including Special Forces troops, participated in the exercise.

After it ended, the small American contingent stayed on and the task force was established at a Jordanian training center north of Amman. It includes communications specialists, logistics experts, planners, trainers and headquarters staff members, American officials said. An official from the State Department’s Bureau of Population, Refugee Affairs and Migration is also assigned to the task force.

Image Credit... The New York Times

“We have been working closely with our Jordanian partners on a variety of issues related to Syria for some time now,” said George Little, the Pentagon press secretary, who added that a specific concern was the security of Syria’s stockpiles of chemical and biological weapons. “As we’ve said before, we have been planning for various contingencies, both unilaterally and with our regional partners.”

Defense Secretary Leon E. Panetta met in Amman in August with King Abdullah II of Jordan and at that time pledged continuing American help with the flow of Syrian refugees. Mr. Panetta was followed in September by Gen. James N. Mattis, the head of Central Command, who met with senior Jordanian officials in Amman.