Damascus suburbs Yarmouk, Eastern Ghouta and Moudamiyah have been besieged by government forces for several months.
The situation has become so desperate that this week Muslim clerics issued a religious ruling - a fatwa - allowing people to eat cats, dogs and donkeys just to survive. Those animals are usually considered unfit for human consumption in Islam.
The clerics said if the situation continued to deteriorate, the living would have to eat the dead.
Similar edicts were announced in Homs and Aleppo when the fighting in those cities was at its fiercest.
US State Department spokeswoman Jen Psaki issued a statement calling on the regime to "immediately approve relief convoys".
She warned that "those who are responsible for atrocities in the Damascus suburbs and across Syria must be identified and held accountable". She added that in Moudamiyah "people have been without basic necessities for nearly a year, and the regime's deliberate prevention of the delivery of life-saving humanitarian supplies to thousands of civilians is unconscionable".
Syrian activists say they are recording the first deaths of complications caused by malnutrition.
Meanwhile, nine Shia pilgrims from Lebanon kidnapped in Syria were freed yesterday as part of a negotiated hostage deal that could result in the release of two Turkish pilots being held in Lebanon.
The pilgrims were part of a group of 11 hostages taken by a rebel faction in northern Syria in May last year. Two were later released, but the nine had been held since, causing friction in the region and sparking an August kidnapping in Beirut in which two Turkish Airlines pilots were abducted.
Lebanese Interior Minister Marwan Charbel said he expects two Turkish pilots to be released in Lebanon soon and the Syrian Government will release a number of female detainees.
