NEW DELHI — A dispute along Nepal’s border with India involving ethnic groups unhappy about the country’s new constitution is stretching into its fifth month, with supplies of fuel and medicine running dangerously low as winter is sets in.

Every day now in Nepal’s capital of Kathmandu, Meena Khadka has to search for firewood to cook her meals.

She has received some kindling passed out by the government, but not enough. And she can’t afford to buy gas cylinders for her stove on the black market, where prices have doubled and tripled in recent weeks.

“This is the hardest time I’ve ever experienced,” said Khadka, 35, a maid who is the sole breadwinner for her family, which includes two sons and a nephew.

The weeks-long protests, which have left nearly 50 dead, also are complicating relief efforts for a country still devastated by earthquakes in April and May. Schools have been shuttered. Hospitals are delaying surgeries. Long lines for fuel are common. Restaurants in Kathmandu have developed special “Blockade Menus” with limited supplies.

The country’s central bank said in a recent report that the unrest could plunge more than 800,000 into extreme poverty.

“Our movements have been obstructed, patients don’t have medicines, our lifeline has been blocked, earthquake victims are sleeping in an open space even in winter and we are not being able to help them,” said Laxmi Prasad Dhakal, a spokesperson for Nepal’s Home Ministry. “Isn’t this a humanitarian crisis?”

On Monday, the United Nations Children’s Fund warned that more than 3 million children younger than 5 were at risk of death or disease over the winter because of the severe shortages — with supplies of vaccines and antibiotics running low.

Rosemarie North, the communications and advocacy manager for the South Asian delegation of the International Federation of Red Cross and Red Crescent Societies, said the group had to begin giving cash to 50,000 households instead of directly distributing blankets and warm clothes because of the fuel shortages.

The dispute began in August, when the country promulgated a new constitution that had been awaited for years. Ethnic groups, including the Madhesis, who have linguistic and cultural links to neighboring India, protested that they weren’t adequately represented. They began a sit-in at a key border crossing with India, causing a bottleneck of supplies to the land-locked nation from its biggest trading partner.

The Nepalis have charged that India, in tacit support of the Madhesis, has restricted its Nepal-bound cargo. The Indians have denied this, saying their trucks are hampered by the protesters.

Vikas Swarup, the spokesman for India’s Ministry of External Affairs, tweeted Wednesday that the external affairs minister, Sushma Swaraj, had met with Nepal’s deputy prime minister and assured him that “there is no hindrance of supplies from India. But Nepal needs to normalize the situation ASAP.”

Meanwhile, the two sides in Nepal show little sign of resolving the constitutional crisis.

The United States has urged the two sides to resolve their differences as the potential for a humanitarian crisis looms. The country’s efforts to use more than $4 billion in international aid has nearly ground to a standstill.

Meanwhile, along the fraught border, Shailendra Tripathi, 29, a Madhesi, said he worries about the psychological effect that the long weeks of protests will have on his four children.

“They are more used to chanting of political slogans than studying,” he said. “They didn’t go to school for three months.”

Classes have resumed to a degree, but only about 40 percent of the students have returned, he said.

“We are in a dilemma now,” he said. “We cannot give up our movement for our rights, nor can we compromise with the future of our children.”

Pradeep Bashyal in Kathmandu and Nick Kirkpatrick in Washington contributed to this report.