According to SANA, Syria's state news agency, 65 trucks loaded with aid supplies entered Madaya and two other besieged towns, Foua and Kefraya.
Four trucks carrying food and blankets had moved into the city by about 5:30 p.m. Monday, the source said. The rest of the 44-truck convoy, carrying medicine and other supplies, was expected to enter the city shortly afterward, the source said.
"It's heartbreaking to see so many hungry people," said Sajjad Malik, the UNHCR representative in Syria. "It's cold and raining but there is excitement because we are here with some food and blankets."
Shocking images of starving residents of the rebel-held city -- under siege by Syrian regime forces and their allies since July -- have drawn international attention.
The situation has been so dire that a doctor told CNN that he has nothing to give his patients except sugar or salt water. In one video posted by Syrian activists, a skeletal boy, his ribs protruding, says he hasn't eaten a full meal in seven days.
The convoy came from the U.N. World Food Programme, International Red Cross and Syrian Arab Red Crescent and had been positioned at the outskirts of the city. It was set to deliver enough aid to sustain 40,000 people for a month, WFP spokeswoman Abeer Etefa said.
The U.N. source told CNN that an equivalent amount of aid would also enter the regime-loyal towns of Foua and Kefraya, in the northern province of Idlib, which were enduring a similar plight while under siege by rebels. The aid trucks were scheduled to progress through both areas throughout the night, the source said.
But International Red Cross spokeswoman Dibeh Fakhr said the aid will go only so far.
"One short delivery will not be the solution," she said. "What is needed is regular access."
Graphic images of death and starvation coming out of Madaya have not been independently confirmed by aid groups or CNN.
But the United Nations said last week that it had received credible reports of people dying of starvation
and that the Syrian government had agreed to allow aid convoys into Madaya, Foua and Kefraya.
Syrian Ambassador to the U.N. Bashar al-Ja'afari denied that anyone is starving in Madaya, calling the images of starving people "fabrications." He said his government had appealed for humanitarian assistance weeks ago.
"The problem is the terrorists are stealing the humanitarian assistance from the Syrian Red Crescent as well as from the United Nations," al-Ja'afari said.
He denied the Syrian government is using starvation as a tool of war, which is generally considered a war crime.
"The Syrian government did not stop any convoys of humanitarian assistance," he said. "On the contrary: We sent plenty of convoys and we asked the U.N. to send more."
When asked about al-Ja'afari's claim, Stephen O'Brien, the United Nations under-secretary-general for humanitarian affairs and emergency relief coordinator, told reporters the United Nations. has "reports of people who are either starving or indeed have starved and died."
"I can tell you that we have had confirmation of extreme malnourishment of a number of people across all ages," he said.
Unbearable costs and landmines
Even though Madaya is less than 50 kilometers (31 miles) from the capital city of Damascus, the cost of food has crippled the city.
For example, in Damascus, flour costs 79 cents a kilogram. But in Madaya, a kilo of flour costs $120, and a kilo of rice costs $150.
In the capital, milk costs $1.06 a liter. But in Madaya, the price soars to $300 a liter.
Then there's the problem of landmines, which have made smuggling food into the city extremely dangerous, Dr. Khaled Mohammed said.
Mohammed, who works at a field hospital in Madaya, said he gets about 250 cases of starvation a day. He said the hospital has seen at least 55 deaths from starvation.
On Sunday, he said five people died in the past 48 hours, including a 9-year-old child.
And when a child dies, the doctor said, it's likely his or her siblings will die soon, too. So families go door to door, urgently trying to gather what they can to feed the siblings.
'The tip of an iceberg'
"These harrowing accounts of hunger represent the tip of an iceberg," said Philip Luther, the Middle East director for Amnesty International.
"Syrians are suffering and dying across the country because starvation is being used as a weapon of war by both the Syrian government and armed groups."
Luther accused both sides of "toying with the lives of hundreds of thousands of people" and said that starving civilians as a tactic in warfare is a war crime.
School bombed from the air
More than 250,000 Syrians have been killed in the civil war
, according to the United Nations, the vast majority dying violently.
On Monday, activists said that 15 people -- including at least 12 children -- had been killed in an aerial bombardment on a school in the town of Enjarah on the western outskirts of Aleppo, the largest Syrian city, which is in the north of the country.
The toll was likely to rise as there were many victims injured, and many remained missing under the rubble, the UK-based Syrian Observatory for Human Rights and activists on the ground told CNN.
An activist described scenes of chaos at the school as he arrived after the strike, about 8 a.m. local time Monday.
"There were many ambulances, people trying to evacuate the area, I saw many body parts (of) children," he said.
"Everyone was trying to find his children."
Eating leaves and grass
But even for those who avoid the bombs, the risk of starving to death continues to grow.
"The last time I had a full meal was at least a month and a half ago," a Madaya resident named Louay said, according to Amnesty International. "Now, I mainly have water with leaves. Winter is here and the trees no longer have leaves, so I am not sure how we will survive."
Louay was interviewed on January 7, along with other Madaya residents.
Um Sultan said she hears every day of someone too sick to leave the bed.
"My husband is now one of them," she told Amnesty. "He can't leave the bed, and when he does, he faints. I don't recognize him anymore; he is skin and bones."
One video shows an old woman stirring a pot of green boiling water. The man filming her asks in Arabic: "Hajji, what are you cooking?"
"Grass for the old man," she replies.