NAIROBI, Kenya (AP) — Ethiopia’s prime minister on Tuesday declared “the final and crucial” military operation will launch in the coming days against the government of the country’s rebellious Tigray region, while the United Nations warned of a “full-scale humanitarian crisis” with refugees fleeing and people in Tigray starting to go hungry.

In a warning to Americans still in the Tigray region, the U.S. Embassy in Ethiopia said those who can't leave safely “are advised to shelter in place.” More than 1,000 citizens of various foreign countries are estimated to be trapped.

Prime Minister Abiy Ahmed said a three-day deadline given to the Tigray region’s leaders and special forces “has expired today.”

Now, "we are marching to Mekele to capture those criminal elements,” Ethiopia's minister in charge of democratization, Zadig Abraha, said in a phone interview with The Associated Press. “This will be a very brief operation.” Mekele, he said, will be the final stage.

Abiy, last year’s Nobel Peace Prize winner, continues to reject international pleas for dialogue and de-escalation in the two-week conflict in the Horn of Africa that has spilled into neighboring Eritrea and sent more than 27,000 frightened Ethiopian refugees pouring into Sudan.

Some 4,000 refugees keep arriving every day, a “very rapid” rate, U.N. refugee agency spokesman Babar Baloch told reporters in Geneva. “It’s a huge number in a matter of days ... It overwhelms the whole system,” he said, adding that the remote part of Sudan hasn’t seen such an influx in two decades.

Inside the Tigray region, cut off from the world with roads and airports closed, food and fuel and medical supplies are running desperately short.

“Our partners warn that supplies will soon be exhausted, putting millions at risk of food insecurity and disease,” spokesman Stephane Dujarric said.

Alarmed African neighbors including Uganda and Kenya are calling for a peaceful resolution, but Abiy’s government regards the Tigray regional government as illegal after it defiantly held a local election in September. The Tigray regional government objects to the postponement of national elections until next year because of the COVID-19 pandemic and considers Abiy's federal government illegal, saying its mandate has expired.

Ethiopia’s federal government on Tuesday also confirmed carrying out new airstrikes outside Mekele, calling them “precision-led and surgical” and denying the Tigray government’s assertion that civilians had been killed.

Tigray TV showed what appeared to be a bombed-out residential area, with damaged roofs and craters in the ground.

“I heard a sound of some explosions. Boom, boom, boom, as I entered the house,” the station quoted a resident as saying. "When I got out later, I saw all this destruction. Two people have been injured. One of the injured is the landlord, and the other is a tenant just like us.”

Communications with the Tigray region remain almost completely cut off, making it difficult to verify either side’s claims.

When asked when communications might resume, the minister, Zadig, asserted, “It's not up to us. The TPLF destroyed telecom infrastructure in Tigray. ... By keeping people incommunicado, they're trying to keep the Tigray people hostage with propaganda.”

He also denied the TPLF assertion that Eritrean forces had joined the conflict at the federal government's request, saying that “there is no foreign government, no foreign army operating inside Ethiopia.” And no foreign government is giving military support from outside, either, he said.

Hungry, exhausted and scared, refugees from the Tigray region continued to flow into Sudan with terrifying accounts of war.

“These people are coming with knives and sticks, wanting to attack citizens. And behind them is the Ethiopian army with tanks. The knives and the sticks aren’t the problem, it’s the tanks," said one refugee, Thimon Abrah. “They struck and burned the entire place.”

“When a man, or even a child is slaughtered, this is revenge,” said another, Tedey Benjamin. “This is a tribal war.”

Ethiopia's prime minister on Monday night said his government is ready to “receive and reintegrate” the refugees and that federal forces would protect them.

But many refugees say those same forces sent them fleeing.

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Associated Press journalists Mohamed Awad in al-Qadarif, Sudan, and Jamey Keaten in Geneva, contributed to this report.