Ethiopian troops appeared to be pushing back militia fighters in the conflict-hit Amhara region, residents of two cities said Wednesday, after local authorities reported that "relative peace" was being restored.

Ethiopian Airlines also announced that it was resuming flights to the northern region's capital Bahir Dar and the city of Gondar from Thursday after suspending operations on Tuesday.

Prime Minister Abiy Ahmed's government last week declared a six-month state of emergency in Amhara after fierce clashes erupted between local fighters and federal troops.

The fresh unrest in Africa's second most populous country comes just nine months after the end of a devastating two-year war in the neighbouring region of Tigray that also drew in fighters from Amhara.

Tensions in Amhara have been rising since April, when the federal government announced it was dismantling regional forces across Ethiopia.

But the Amhara regional administration issued a statement late Tuesday saying that calm was being restored.

"The violence that happened recently in some areas of our region, which was aided by extremist and predatory power-hungry groups, is returning to relative peace and stability in all areas of the region," it said.

Local residents contacted by AFP on Wednesday said federal troops appeared to be pushing back militia fighters in Gondar and Lalibela, a UNESCO World Heritage Site famous for its ancient rock-hewn churches.

"Things seem to be changing today," said Simachew, a rickshaw driver in Gondar.

The Ethiopian army "is taking control of most parts of the city after heavy fighting for the past couple of days. The engagement was supported by tanks and armoured vehicles, which are still in the city".

He said Fano militants were "now restricted" to one area of the city and that fighting was ongoing there.

A resident of Lalibela who gave his name only as Ayalew said the Ethiopian army was now based on the city's airport road.

"Fano has left the city and are in the forest," he said, adding that there was no movement in the city.

"We only hear heavy artillery sounds being fired."

Access to Amhara is restricted for journalists and it is not possible to independently verify the situation on the ground.