Eritrea's capital came under fire from Ethiopia's breakaway Tigray region Friday, raising fears that Ethiopia's internal conflict could spread as leader Abiy Ahmed resisted calls for dialogue.

People continued to flee the capital of Ethiopia's embattled Tigray region in fear of an imminent assault after Prime Minister Abiy Ahmed said the army had been ordered to move in for the "final phase" of an offensive to arrest the defiant regional leaders.

Fighting reportedly remained well outside Mekele, a densely populated city of a half-million people who had been warned by the Ethiopian government of "no mercy" if they didn't separate themselves from the Tigray leaders in time. Abiy on Thursday told residents to stay indoors and disarm as the army, with tanks, was given the order to move in. His government has vowed to protect civilians.

Prime Minister Abiy Ahmed on Thursday ordered Ethiopia's army to launch a final offensive against Tigray's leaders in their regional capital Mekele, saying the window for their surrender had expired.

Ethiopia's prime minister is rejecting growing international consensus for dialogue and a halt to deadly fighting in the Tigray region as "unwelcome," saying his country will handle the conflict on its own as a 72-hour surrender ultimatum runs out on Wednesday.

"We respectfully urge the international community to refrain from any unwelcome and unlawful acts of interference," the statement from Prime Minister Abiy Ahmed's office said as government forces encircled the Tigray capital, Mekele, with tanks. "The international community should stand by until the government of Ethiopia submits its requests for assistance to the community of nations."

The UN Security Council will on Tuesday hold its first meeting on the conflict in Ethiopia's dissident Tigray region, diplomatic sources said.

International pressure mounted Tuesday on the warring parties in northern Ethiopia to cease fighting and protect civilians in Tigray, whose leaders Prime Minister Abiy Ahmed has given a deadline to surrender.

Ethiopia's government claimed advances in its battle against the dissident Tigray region on Saturday, while showing no signs of bowing to international pressure for a halt to the conflict that has caused tens of thousands to flee and raised fears of a humanitarian disaster.

Tigray forces fired rockets at a neighboring state on Friday, heightening fears the internal conflict could spread to other parts of the country, a day after Ethiopia said its forces were closing in on the dissident region's capital Mekele.

Ethiopia's army chief on Thursday accused WHO boss Tedros Adhanom Ghebreyesus -- the country's highest-profile Tigrayan abroad -- of lobbying in favour of the dissident region and helping them get weapons.

Ethiopian Prime Minister Abiy Ahmed said Tuesday military operations in the northern Tigray region would enter a "final" phase, as global pressure mounted to bring the two-week-old conflict to a swift end.