Syria's government has authorized UN aid deliveries to the towns, including Madaya, which is northwest of Damascus and near the Lebanese border.
At least 23 people in a health center there supported by Medecins Sans Frontieres have starved since December 1, the group said on its website, adding that many more are at risk. Six of the dead were aged one year or less.
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A first round of relief deliveries was expected to arrive over the weekend, UN officials said.
Madaya, surrounded by pro-government forces, is in dire need of medical supplies as well as food. The other two towns, Fuaa and Kafraya in the northwest, are besieged by rebels.
Spain and New Zealand on Friday asked that the 15-member council receive a report Monday on the UN aid effort.