The United Nations Refugee Agency (UNHCR) warned on Tuesday that the situation at the Libya-Tunisia border was reaching a "crisis point" as more people fleeing violence arrive in the area, dpa reported.
The International Committee of the Red Cross meanwhile warned that it still did not have access to vast swathes of Libya, two weeks after the crisis began.
"It is high time people's humanitarian needs are met and humanitarian agencies can enter into rest of the country and help those in need," said ICRC spokeswoman Anna Nelson, urging both sides in Libya not to attack patients and doctors.
The UN Office for the Coordination of Humanitarian Affairs (OCHA) said that the largest concern was for the west of Libya, where access and information were very limited. In Benghazi in the east, the situation was said to be calm and aid was being accepted.
Melissa Fleming, a UNHCR spokeswoman in Geneva, said authorities, including humanitarian workers, were "seriously overstretched," especially on the Tunisian side of the border area in the west.
Prior to the crisis, there were an estimated 1.5 million migrant workers in Libya.
UN agencies said concern was mounting for the safety of those workers from sub-Saharan Africa, who are in the most precarious situation, are being hunted down and have largely not been evacuated.