The bid by the Kafficho ethnic group to form a new federal state risks further destabilising Ethiopia's diverse southern region, which just two months ago was rocked by violence stemming from a similar campaign by the Sidama ethnic group.
Ethiopia is currently partitioned into nine semi-autonomous regions. The constitution requires the government to organise a referendum for any ethnic group that wants to form a new entity.
At least 11 groups have submitted such bids in the south, and Abiy is at pains to prevent further tensions ahead of elections next year.
"If you think that statehood will solve your problems, that's a shortcut," Abiy told a packed town hall Sunday in Bonga, the main town in Kaffa, the zone where the Kafficho are concentrated.
Officials in Kaffa passed a resolution in favour of breaking away last November, claiming they have been deprived of resources allocated by the federal government.
"The arguments you raised are rational. They should be taken into consideration," Abiy said, adding regional concerns would take more than "one meeting".
A crowd numbering in the thousands chanted the prime minister's name as he arrived wearing sunglasses and a white coat bearing the traditional Kafficho colours of red, green and blue.
Abiy vowed to address concerns about lack of development and asked the crowd to join him in building "a great Ethiopia".
But while Abiy spoke of national unity, local officials talked up the history of the local Kaffa kingdom, which ruled from the 14th century until the late 19th century.
"My interest is the people's interest, and the people want a new state," said local official Dawud Mohammed.
Abiy's administration has been faulted for its handling of the campaign to form a new region in the Sidama zone.
In that case, the government failed to organise a referendum on time. In July, tensions spilled over into violent clashes between activists and security forces that killed at least 18 people.
In a bid to restore order, federal security forces took over in the southern region, which accounts for one-fifth of the country's 110 million people.
The government has now promised the Sidama referendum will take place in November.
William Davison, a senior analyst for the International Crisis Group think tank, said the government "faces a dilemma" on how to handle the other requests.
"Proceeding with additional referendums would increase pressure on the fragile ruling coalition, and could also trigger local conflicts over political power and resources," he said.
"Yet trying to hold the rest of the south together is likely to necessitate political coercion and forcibly repressing popular protests."