UNITED NATIONS — The U.N. Security Council unanimously approved a resolution Monday authorizing cross-border delivery of humanitarian aid to Syrians in rebel-held areas in desperate need of food and medicine, without government approval.

U.N. humanitarian chief Valerie Amos said several weeks ago that opening these routes could help 1.3 million Syrians – and her office said Monday that if security allows, aid could reach 2.9 million people.

The resolution, a rare agreement on Syria, expresses “grave alarm at the significant and rapid deterioration of the humanitarian situation in Syria.” It deplores the fact that the council’s previous demands for humanitarian access “have not been heeded” by the government and opposition fighters.

The United States and many European council members said the resolution would not have been necessary if the Syrian government, especially, had complied with a February resolution demanding that all sides allow immediate access for aid.

Since February, however, President Bashar Assad has continued to bar cross-border deliveries to rebel areas and insisted that all shipments go through the capital Damascus, which has meant the overwhelming majority of aid has gone to government-controlled areas.

Monthly reports to the council since February by U.N. Secretary-General Ban Ki-moon on the resolution’s implementation have described an increasingly dire situation.

Amos said in June that the number of Syrians in need of humanitarian assistance has increased from 1 million in 2011 to 10.8 million, jumping 1.5 million in just the last six months. That includes 4.7 million in hard-to-reach areas, and over 240,000 trapped in besieged areas.

The resolution adopted Monday takes steps to overcome the Syrian government’s opposition.

The U.N.’s most powerful body authorized U.N. agencies and aid organizations that assist them to deliver humanitarian assistance across conflict lines between government and rebel forces and through four border crossings – two in Turkey, one in Iraq and one in Jordan – without government approval. It authorizes the United Nations to monitor the loading of all aid shipments in the three countries before they cross the Syrian border.