NAIROBI, Kenya (AP) — Ethiopia's military launched an offensive on the Tigray regional capital Saturday in a quest to arrest the region’s defiant leaders, and the city was being “heavily bombarded,” Tigray TV reported.

Humanitarians confirmed the shelling in Mekele, a densely populated city of a half-million people, which immediately raised concerns about civilian casualties. The Tigray leader could not be reached, and Ethiopia’s government did not comment.

Ethiopia’s government had warned Mekele residents there would be “no mercy” if they didn’t move away from the leaders of the Tigray People’s Liberation Front in time. The United Nations said some residents fled as the military closed in.

“The United States is gravely concerned about the worsening situation in the Tigray region,” the U.S. ambassador to the U.N., Kelly Craft, tweeted after the reported bombardment began. She called for dialogue, the protection of civilians and access for aid.

“I invite everyone to pray for Ethiopia where armed clashes have intensified and are causing a serious humanitarian situation,” Pope Francis tweeted.

Communications remain largely severed to the Tigray region of some 6 million people, making it difficult to verify claims by the warring sides in the conflict between Ethiopia’s government and the TPLF, which once dominated the country’s ruling coalition but was sidelined under new Prime Minister Abiy Ahmed.

Abiy has rejected dialogue with the TPLF, most recently in his meeting on Friday with African Union envoys. Each government regards the other as illegal.

The offensive on Mekele has alarmed the international community. Abiy’s government has said it would take care to avoid harming civilians in the tank-led assault.

As Ethiopian forces moved in, Maj. Gen. Hassan Ibrahim vowed to capture the city “on all fronts.”

“It is possible that some of the wanted people may go to their families or neighboring areas and try to hide for few days. But our armed forces, after seizing control of Mekele city, will be tasked to hunt down and capture these criminals one by one wherever they may be,” he said in comments carried by the Ethiopian News Agency.

The Tigray region has been almost entirely cut off from the outside world since Nov. 4, when Abiy announced a military offensive in response to a TPLF attack on a military base. Humanitarians have said at least hundreds of people have been killed.

The fighting threatens to destabilize Ethiopia, which has been described as the linchpin of the strategic Horn of Africa.

With transport links cut, food and other supplies are running out in Tigray, home to 6 million people, and the United Nations has asked for immediate and unimpeded access for aid.

Nearly 1 million people have been displaced in the region, the U.N. said in an update Saturday, citing local authorities.

The office of U.N. Secretary-General Antonio Guterres said he has “expressed his grave concern over the consequences of the Ethiopian conflict to the civilian population and over the spread of hate speech and reports of ethnic profiling.”

Multiple crises are growing. More than 43,000 refugees have fled for Sudan, where people struggle to give them food, shelter and care. The International Committee of the Red Cross says hospitals in Tigray are running out of drugs. And fighting near camps sheltering 96,000 Eritrean refugees in northern Ethiopia has put them in the line of fire.

U.N. High Commissioner for Refugees Filippo Grandi on Saturday visited Sudan’s Umm Rakouba refugee camp, which houses some 10,000 refugees. He said about $150 million is needed over the next six months to help Sudan manage the influx.

Worryingly, refugees in Sudan have told The Associated Press that Ethiopian forces near the border are impeding people from leaving. Reporters from the AP saw crossings slow to a trickle in recent days. Ethiopia’s government has not commented.

“We have seen the figure of people decline but continuing. Five to 600 per day is not a small figure, let’s make no mistake. It is true there were days in which they were in their thousands, but it depends also on the difficulty of moving around their country and on the border," Grandi said.

Access to Tigray is “the main obstacle at the moment," he said, urging Abiy's government to "grant us corridors or whatever they call it to provide assistance.”