Desperate Syrians are fleeing their country in growing numbers, some even being shot at from behind as they abandon their cities and villages.

"In the course of just one night nearly 1,300 civilians arrived at Turkish camps and there are now reports of upwards of 8,500 Syrians who crossed the border into Lebanon in the last 24 hours," said Kelly Clements, deputy assistant secretary of state for the Bureau of Population, Refugees and Migration.

Clements joined Maria Otero, under secretary of state for civilian security, democracy, and human rights, and Mark Bartolini, director of the Office of Foreign Disaster Assistance, to brief reporters by phone Thursday on U.S. efforts to provide aid to civilians still in Syria and to refugees who are flowing over the Syrian border into the neighboring countries of Turkey, Iraq, Jordan and Lebanon.

Currently, the officials say, there are 42,600 Syrian refugees in Turkey in camps along the border, 37,000 in Jordan, 32,500 in Lebanon and 8,000 in Iraq.

Another 1.5 million Syrians need humanitarian help inside the country, they said.

"Inside Syria, lack of access due to violence by all parties remains the number one limiting factor for humanitarian assistance," Clements said. "International humanitarian agencies simply are unable to reach those most in need. We urge all parties to facilitate unimpeded access to affected areas and populations for humanitarian agencies."

Bartolini said from 300,000 to 500,000 Syrians have been displaced from their homes. Providing aid is "incredibly difficult," he said, and there are numerous reports of aid workers being harassed, killed and taken captive.

So far, the United States has provided $64 million in humanitarian assistance and officials say "more is coming."

The United States is working through international aid organizations because those groups already had staff and structures in place in Syria and neighboring countries prior to the conflict. Those organizations include the Syrian Arab Red Crescent, UNICEF, the International Committee of the Red Cross, the World Food Program, the U.N. High Commissioner for Refugees and the United Nations Relief and Rehabilitation Administration.

During her visits to Turkey and Jordan, Otero said, she saw men, women and children in need of food, medical help and psychological counseling. Some had been wounded in the fighting, and some had missing limbs.

Otero said she met with a woman who had been hit with a bullet that went through her eye and out her cheek.

"There are really heroic efforts going on right now inside of Syria to help people most in need," Bartolini added. "We are having an impact. We are not reaching everyone but we are doing the best we can and are hopeful we will get more access."