The prime minister's spokesman Billene Seyoum told Reuters later that military operations in Tigray had commenced, without elaborating.
Two diplomatic sources in Addis Ababa said heavy fighting, including artillery fire, had broken out in the northern region, which borders Eritrea.
Tigray's local government said the Northern Command of the federal military, which is stationed in the region, had defected to its side, a statement which Billene described as "false information".
The prime minister's office said the federal government had declared a six-month state of emergency in Tigray to be overseen by the chief of staff of the armed forces.
The internet was shut down in the region, internet access monitor NetBlocks said, confirming reports that authorities had shut down telephone and internet services.
Tigrayans dominated Ethiopian politics after guerrilla fighters ousted a Marxist dictator in 1991, but their influence has waned under Abiy. Last year, the TPLF quit his ruling coalition.
Since Abiy came to power in 2018, many senior Tigrayan officials have been detained, fired or sidelined, in what the federal government describes as a clamp-down on corruption but Tigrayans see as a means to quell dissent.
Tigray's population makes up 5% of Ethiopia's 109 million people, but it is wealthier and more influential than many other, larger regions.