The state-affiliated Ethiopian Human Rights Commission (EHRC) said there were “no serious or widespread human rights violations” in stations it observed.
However, in a preliminary report the EHRC said that some constituencies experienced “improper arrests”, voter intimidation and “harassment” of observers and journalists.
It also said it had observed several killings in the days leading up to the vote in the regional state of Oromia.
In May, the EU accused Ethiopia of failing to guarantee the independence of its election.
The election was Abiy’s first electoral test since coming to power in 2018.
He has clamped down on corruption, released political prisoners, appointed more women to the cabinet and made peace with neighbouring Eritrea, following a 1998-2000 border war that left tens of thousands of people dead.
He won the 2019 Nobel Peace Prize, but just a year later waged a military operation in his own country – deploying troops to the northern Tigray province to oust the TPLF as the region’s ruling party after it seized military bases in what Abiy saw as a bid to overthrow him.
The conflict in Tigray has killed thousands of people and led to mass hunger and reports of a famine in the region.
On Saturday, for the first time in two weeks, the UN World Food Programme began moving aid into Tigray. Different sides in the conflict have been accusing each other of blocking much-needed shipments.
The UN said on Friday that humanitarian operations were being constrained by the absence of essential services including fuel, telecommunications and electricity.