Ugandan President Yoweri Museveni held talks with Ethiopia's deputy prime minister Demeke Mekonnen, while former Nigerian president Olusegun Obasanjo headed to Addis Ababa to make his bid for dialogue.

Ethiopian Prime Minister Abiy Ahmed announced November 4 he had ordered military operations in Tigray in a dramatic escalation of a long-running feud with the region's ruling party, the Tigray People's Liberation Front (TPLF).

Hundreds of people are reported to have been killed so far in the conflict in Africa's second most populous country, some in a gruesome massacre documented last week by Amnesty International.

More than 25,000 Ethiopians have fled into Sudan, Sudanese officials say.

"A war in Ethiopia would give the entire continent a bad image," Museveni wrote on Twitter after meeting Demeke in the northern town of Gulu.

"There should be negotiations and the conflict stopped, lest it leads to unnecessary loss of lives and cripples the economy."

Meanwhile Nigeria's ex-president Obasanjo on Monday left for Addis Ababa to mediate in the crisis, his spokesman said.

"Yes he is on his way to Addis Ababa for talks," Kehinde Akinyemi told AFP on the visit of the former Nigerian leader to the Ethiopian capital.

"He is going there for mediation," he said, without giving further details.

Both Abiy's office and the African Union said Monday they did not have information about Obasanjo's visit.

Abiy's office also denied any talks were taking place in Uganda.

"The claims by various news outlets that Ethiopian officials are expected to take part in mediation talks with TPLF in Uganda is inaccurate and not substantiated," a government statement said.

TPLF leader Debretsion Gebremichael told AFP Monday he was "not aware" of Museveni's initiative.

- Restoring order -

Abiy's government has said the TPLF needs to be disarmed before negotiations can begin, as world leaders have called for an immediate end to hostilities.

On Monday the House of Federation, the upper house of parliament, said in a statement that calls for talks were misguided because the government and the TPLF are "by no means on equal legal and moral footing".

"The fact of the matter is that it is the TPLF which has violated the constitution and endangered the constitutional order. The federal government is merely working towards restoring it," the statement said.

Ethiopian military officials have vowed to keep military operations contained in Tigray, and Abiy has repeatedly vowed to deliver a quick, decisive victory.

Last week Abiy said federal forces had "liberated" the western zone of the Tigray region, which is made up of six zones plus the capital, Mekele, and surrounding areas.

On Sunday state media reported that federal forces had seized Alamata, a town 180 kilometres south of Tigray.

"As the TPLF militia were defeated in Alamata, they fled taking along around 10,000 prisoners," a government statement said.

A communications blackout in Tigray has made claims of advances difficult to verify.

- Fears of wider conflict -

In recent days the TPLF has extended the conflict beyond Tigray, launching rockets on airports in Ethiopia's Amhara region, which borders Tigray to the south, and in the capital of Eritrea, Ethiopia's neighbour to the north.

Debretsion has said the strikes are "legitimate" because federal forces are using the airports as part of their military operations in Tigray.

The strikes on the Eritrean capital Asmara in particular have reinforced fears that Ethiopia's conflict could draw in the wider Horn of Africa region.

The TPLF has accused Abiy's government of enlisting military support from Eritrea, something Ethiopia denies.

Debretsion said Sunday that TPLF forces had been fighting "16 divisions" of Eritrean forces in recent days "on several fronts".

On Sunday night Tibor Nagy, the US State Department's top diplomat for Africa, said Washington "strongly condemns the TPLF's unjustifiable attacks against Eritrea on November 14 and its efforts to internationalise the conflict in Tigray".

"We continue to urge immediate action to protect civilians, de-escalate tensions, and restore peace," Nagy said in a Twitter post.