Russia has recently called for the Rukban camp near the Jordanian border to be dismantled and accused the U.S. of hindering such efforts. In the past, Russia and Syria have accused the U.S. of blocking aid delivery.
Speaking in Jordan on Sunday, Russia's Foreign Minister Sergey Lavrov called the U.S. presence in the area "unlawful," saying it has "unilaterally" created "some kind of safe zone."
The camp, which is surrounded by areas controlled by the Syrian government, lies within a "de-confliction zone" agreed to by the U.S. and Russia.
Col. Scott Rawlinson, a spokesman for the U.S. military, said Monday that the U.S. military has stressed to the Russians the "importance" of the zone "in clear and unambiguous terms."
The U.S. "expects all parties to abide by this (de-confliction) agreement," he said in an email to The Associated Press.
Rawlinson said the U.S. supports efforts by the United Nations to improve conditions for the over 40,000 people housed in Rukban camp. He said their departures from the camp should be "safe, informed and voluntary."
U.N. officials have said most of Rukban's residents want to leave, but fear for their security and need more safety guarantees.
At least 400 camp residents left Sunday toward shelters provided by the government in central Homs province, bringing the total of those who left since March 24 to 1,660 people, according to the U.N.
The last aid delivered to Rukban was two months ago. Jordan has closed its borders with the camp, citing security concerns. For a period, aid used to be delivered across sand berms from Jordan, until the first shipment of aid arrived to the camp from Damascus in February.