Conflict broke out there 11 months ago between federal troops and forces loyal to the Tigrayan People's Liberation Front (TPLF), the political party that controls Tigray.
Thousands have died and more than two million people have been forced to flee their homes.
On Thursday, Ethiopia announced it was expelling seven senior United Nations officials and gave them 72 hours to leave, a move the UN rejected.
Ethiopia accused the UN officials of diverting aid and communication equipment to the TPLF, failing to demand the return of aid trucks deployed to Tigray, violating security arrangements and spreading misinformation.
The United States also condemned the expulsions and warned that it would not hesitate to use unilateral sanctions against those who obstructed humanitarian efforts.
Mr Abiy was appointed prime minister by the then-governing coalition in 2018 and promised political and economic reforms.
Within months of taking office, he lifted a ban on opposition parties, released tens of thousands of political prisoners and took steps to open up one of Africa's last untapped markets.
His government now faces accusations from rights groups that it is rolling back some new freedoms, which it denies.
In June's vote, Mr Abiy's Prosperity Party won 410 of the 436 parliamentary seats that were contested, out of a total 547 seats. Security and logistical problems delayed voting in the other 111 seats.
The opposition parties Ezema and the National Movement of Amhara (NAMA) each won fewer than 10 seats in the June vote.
On 30 September, an additional 47 constituencies voted. Results from those regions have yet to be announced, but will not affect the overall result.