* Tigrayan capital Mekelle fell to federal troops at weekend
* TPLF leaders say they are still fighting from the mountains
* PM Abiy's government promises to bring peace, aid to Tigray
* Month-long war has shaken already volatile region of Africa
The leader of Ethiopia's rebellious Tigrayan forces said on Friday that protests were breaking out in the regional capital which fell to federal troops days ago in their month-long war.
However, state TV showed images of people shopping and sitting on stools in Mekelle, while the new government-appointed chief executive of Tigray said peace was returning to the area.
Fighting between Prime Minister Abiy Ahmed's federal army and forces loyal to the region's former ruling party, the Tigray People's Liberation Front (TPLF), has raged since Nov. 4.
With communications largely down and access for media restricted, claims from all sides have been impossible to verify. But thousands of people are believed to have died while more than 45,000 refugees have crossed to neighbouring Sudan.
TPLF leaders, who have enjoyed strong popular support for years in Tigray, appear to have fled to surrounding mountains and begun a guerrilla-style resistance.
TPLF No. 1 Debretsion Gebremichael, the most wanted man in Ethiopia, told Reuters in a text message on Friday that there were popular protests in Mekelle, which is home to 500,000 people, due to looting by Eritrean soldiers.
"Eritrean soldiers are everywhere," he said, repeating an accusation that President Isaias Afwerki has sent soldiers over the border to back Abiy against their mutual foe.
Both Ethiopia and Eritrea have denied that.
"Our people in town are protesting their looting. We do have captives but we'll gather more visual evidences," added Debretsion, a 57-year-old former guerrilla radio operator who was once in a coalition government with Abiy.
He gave no evidence of looting or the presence of Eritreans.
Abiy's spokeswoman Billene Seyoum said she would not comment on unverifiable text messages. Previously, she has called them the "delusions of a criminal clique".
The United Nations and aid agencies are extremely worried about the humanitarian crisis in Tigray, where hundreds of thousands of people relied on food aid even before the war.
Charitable organizations say food, fuel, medicines and even bodybags are running low. Convoys are on standby.
Mulu Nega, appointed by Abiy as chief executive of a new Provisional Administration of Tigray, said the government was channelling help to parts of west Tigray including the towns of Humera, Dansha and Mai Kadra.
"Our priority in the region now is to restore peace, stability and order," the 52-year-old former academic told state-run EBC.
Abiy took office two years ago after nearly three decades of TPLF-led government following the overthrow of Marxist dictator Mengistu Haile Mariam in 1991.
He began opening up a closed economy and repressive political system, won a Nobel Peace Prize for a peace pact with Eritrea and took action over past rights abuses and corruption.
But the particular targeting of Tigrayan officials irked the TPLF and Abiy's initially glowing international reputation has come under scrutiny with the jailing of opposition figures and now his offensive against the northern region.
The TPLF accuses their ex-military comrade and political partner of trying to increase his personal power over Ethiopia's 10 regions. Abiy denies that, calling them criminals who mutinied against federal authority, attacked a military base, and were unfairly over-represented in government for a group that only accounts for 6% of the population.
At a US Congressional online hearing on Ethiopia late on Thursday, politicians expressed anxiety about instability both for an important US ally and the wider east Africa region.
"There is a concern ... that the fall of the capital does not necessarily mark the end of the armed conflict," said Republican legislator Chris Smith. "We're very worried, all of us, about a protracted civil war."