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"The final critical act of law enforcement will be done in the coming days," Prime Minister Abiy Ahmed said.
Later that day, Abiy's special task force on the Tigray conflict accused rebel forces of destroying bridges connecting the regional capital Mekelle with the rest of the country in attempts to hold back federal government forces.
"Anxious about (our) advance, the junta has destroyed four bridges that lead to Mekelle," it said, adding that the TPLF had also destroyed the section of a main road eastwards to Mekelle between the towns of Shire and Axum. Shire was under federal control, the task force reported earlier in the day.
"The TPLF junta will soon be held accountable for destroying this infrastructure and for crimes it has committed so far."
There was no immediate TPLF comment on the accusations.
Abiy, Africa's youngest leader and the 2019 Nobel Peace Prize winner, launched air strikes and a ground offensive on November 4 after accusing ex-comrades and the local ruling party, the Tigray People's Liberation Front (TPLF), of armed revolt.
Tigrayan leaders say Abiy (44), who comes from Ethiopia's largest ethnic group the Oromo, has persecuted and purged them from government and security posts since taking office in 2018.
Tigrayan forces have fired rockets into the neighbouring nation of Eritrea, accusing Eritrean forces of helping the Ethiopian government side, an allegation denied by Asmara.
But the rocket fire has escalated a conflict which has already killed hundreds - one diplomatic source said thousands - and sent about 30,000 refugees into Sudan.
"How could they kill their own brothers and sisters? This is not our custom," Addis Ababa resident Fitawrari Million said of the Tigrayan leaders during a rally to honour federal soldiers.
The United Nations said a "full-scale humanitarian crisis" was unfolding. With communications largely down and media barred, Reuters could not independently verify assertions by either side nor the situation on the ground.
"People are coming out of Ethiopia really scared, afraid, with stories saying they have been fleeing heavy fighting and there's no sign of the fighting stopping," said Babar Baloch, spokesman for the United Nations High Commissioner for Refugees (UNHCR).
With hundreds of thousands of Tigrayans dependent on food aid even before the conflict, suffering is worsening as hundreds of humanitarian workers are pulling out for their own safety.
Mark Lowcock, U.N. Undersecretary General for Humanitarian Affairs and Emergency Relief Coordinator, said the United Nations was pressing Abiy's government to assure immediate and safe access to displaced people. "Humanitarian workers must be able to deliver assistance without fear of attack," he said.
'BRING JUNTA TO JUSTICE'
Abiy's air force struck unspecified TPLF targets outside Mekelle on Monday.
Earlier on Tuesday, his task force said federal forces had "liberated" the Raya, Chercher, Gugufto and Mehoni localities on the eastern front, and Shire on the conflict's western front.
Federal forces had also destroyed TPLF military bases in both areas and were now heading towards Mekelle, the statement said. "The force of the junta is now retreating, and the army is marching to bring the TPLF junta to justice."
Tigray's leaders have accused federal forces of knocking out a dam and a sugar factory as well as "mercilessly" attacking people in the region of more than 5 million.
The government denies targeting civilians.
In a sign the push towards Mekelle may not be going entirely to plan, TPLF leader Debretsion Gebremichael told Reuters battles were still ongoing around the southern town of Alamata that federal troops said they seized the previous day.
After Amnesty International reported a massacre of scores of labourers, where it cited witnesses blaming TPLF forces, the United Nations human rights chief said war crimes may have been committed.
Governments around Europe and Africa are clamouring for talks and even the Nobel committee voiced concern in rare comment on a past laureate's actions.
But Abiy has said he will only negotiate when rule of law is restored in Tigray, whose leaders are former military comrades whom he also partnered in government until 2018.
On Monday, his foreign minister went to Uganda and Kenya, while a Nigerian former president flew to Addis Ababa. Diplomats described a growing push for negotiations, but Ethiopia said it was simply explaining an internal conflict to outsiders.
The fighting could jeopardise the recent opening up of Ethiopia's economy, stir ethnic bloodshed elsewhere around the vast nation of 115 million people, and tarnish the reputation of Abiy.
He won his Nobel for pursuing peace with Eritrea and had drawn praise for opening up a repressive political system, though arrests and media curbs have tainted that of late.