(AFP) - 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.

For more than three weeks now, Ethiopia and Tigray have engaged in fierce fighting that the International Crisis Group said Friday had left thousands dead "including many civilians as well as security forces".

On Friday night, at least one rocket fired from the northern Tigray region targeted neighbouring Eritrea, four regional diplomats told AFP.

Abiy, the winner of last year's Nobel Peace Prize, announced Thursday a "third and final phase" in his campaign against leaders of the Tigray People's Liberation Front (TPLF).

Global concern remains centred on the half a million residents of Mekele, Tigray's regional capital, which the army says it has encircled ahead of the threatened attack.

World leaders and human rights groups have warned such a strike could violate rules of war and were calling for urgent mediation.

Pope Francis was among those worried about the intensifying fighting, growing loss of life and displacement, Vatican media head Matteo Bruni said Friday.

Abiy announced military operations in Tigray on November 4 after months of friction between his government and the TPLF, which dominated Ethiopian politics for nearly three decades before Abiy took office in 2018.

The prime minister has refused to negotiate with the TPLF and dismissed calls for dialogue as "interference" in Ethiopia's internal affairs.

On Friday he met with three African ex-leaders -- Joaquim Chissano of Mozambique, Ellen Johnson Sirleaf of Liberia and Kgalema Motlanthe of South Africa -- dispatched this week by the African Union as mediators.

- 'Enforce rule of law' -

In a statement issued after their meeting in Addis Ababa, Abiy said he appreciated "this gesture and... the steadfast commitment this demonstrates to the principle of African solutions to African problems".

Even so, the government has a "constitutionally mandated responsibility to enforce rule of law in the region and across the country," his office said in a statement.

"Failure to do so would further a culture of impunity with devastating cost to the survival of the country," it said.

UN chief Antonio Guterres welcomed the talks with the AU envoys and urged all parties to "peacefully resolve the conflict".

The UN Secretary-General also stressed the need "to ensure the protection of civilians, human rights and access for humanitarian assistance to the affected areas".

The Tigrayan government, meanwhile, said Friday the federal army was bombarding towns and villages and inflicting heavy damage, although it did not specifically mention Mekele.

"Our struggle will continue from every direction until the self-determination of the People of Tigray is guaranteed and the invading force is driven out," Tigrayan authorities said in a statement read on regional television.

A communications blackout in Tigray has made it difficult to verify claims from both sides on the fighting.

Hostilities have erupted in a year when the 55-member AU -- which is headquartered in Addis Ababa -- resolved to play a more prominent role in resolving conflicts across the continent under the slogan "Silencing the Guns".

- Fresh strike on Eritrea -

At least one rocket fired from Tigray targeted neighbouring Eritrea Friday night, four regional diplomats told AFP, the second such attack since Ethiopia's internal conflict broke out earlier this month.

There was no immediate confirmation of how many rockets were fired, where they landed, and any casualties or damage caused.

The TPLF has accused Ethiopia of enlisting Eritrean military support in the fighting, a charge Ethiopia denies.

The group claimed responsibility for similar strikes on Eritrea two weeks ago, but there was no immediate comment from its leaders Friday.

Abiy, who ordered the "final" offensive on TPLF forces in Mekele after the lapsing of a deadline for their surrender earlier this week, said "great care" would be taken to protect civilians and spare the city from severe damage.

- Humanitarian crisis -

The prospect of a full-scale attack accelerated diplomatic efforts this week to resolve the conflict, with the UN Security Council holding its first meeting on Tigray and US and European officials urging restraint.

French Foreign Minister Jean-Yves Le Drian, who met his Ethiopian counterpart Demeke Mekonnen in Paris on Thursday, called for urgent measures to protect civilians as the humanitarian fallout from the crisis worsened across the region.

The UNHCR said Friday that nearly 100,000 Eritrean refugees in Tigray could run out of food as early as Monday if supplies could not reach them.

In eastern Sudan, meanwhile, where more than 40,000 refugees have escaped the fighting in Tigray, local authorities are struggling to meet the sudden surge in demand for food, shelter and other life-saving essentials.

© Agence France-Presse