It has declared the Tigray elections illegal, saying that only the national electoral board has the power to organise polls.
However, Mr Abiy has ruled out sending federal troops into the region to stop the election, saying it would be "madness" to do so.
"The federal government has no intention and interest to attack its own people," he said on 25 July.
But pro-Abiy hardliners, including former army General Kassaye Chemeda, have called for military intervention in Tigray.
"The government should plan well, and they should be attacked," he said in an interview with the government-affiliated Walta TV.
The International Crisis Group (ICG) think-tank says that some federal officials have raised the possibility of retaliating by taking "punitive" action against the Tigray government - for instance, by withholding financial grants, which amount to half the region's budget.
Responding to a call by the upper house of the federal government to meet on Saturday to discuss Tigray's election, the regional government warned that any decision to stop or disrupt the regional election is "tantamount to declaration of war". Furthermore, Tigrayan members of the upper house said they would boycott the meeting.
Why have relations soured so much?
The TPLF - which was extremely influential in the federal government since Marxist rule ended in 1991, with its leader, Meles Zenawi, serving as prime minister from 1995 to 2012 - has keenly felt the loss of power under Mr Abiy.
It saw the prime minister's widely welcomed campaign to end human rights abuses and corruption as a victimisation of TPLF members, especially after senior military and security officers were either purged or arrested soon after Mr Abiy took office in 2018 following mass protests against the former regime.
Ex-spy chef Getachew Assefa managed to evade arrest after reportedly fleeing to Tigray.
The TPLF's influence at the centre weakened even further after Mr Abiy launched the Prosperity Party (PP) - a merger of ethnically-based parties that used to form the ruling coalition.
The TPLF refused to join the PP, leaving it without any influence in the federal government for the first time since Marxist rule ended. Mr Abiy sacked some of its members from the cabinet, while others resigned.
As a result, the TPLF has increasingly retreated to its regional headquarters, Mekelle, raising concerns that its ties with the rest of Ethiopia were loosening.
The federal government crackdown following Hachalu's killing has also fuelled what some analysts call a siege mentality within the TPLF.
Security forces raided and closed the office of a TPLF-affiliated television station, Dimtsi Woyane, in the capital. They also shut the Oromo Media Network's television station, which is linked to detained opposition politician Jawar Mohammed.
Federal and PP officials accused the TPLF of involvement in Hachalu's murder, and of "working to destabilise the country".
The TPLF responded by saying that the party was being scapegoated for Mr Abiy's "incompetent rule" and the "mess created by his administration".
How serious is the threat of secession?
The TPLF played a pivotal role in the overthrow of the Marxist regime in 1991, and the drafting of the constitution that gives ethnic groups the right to self-determination and their own state. Although the party has never expressed any desire for Tigray to secede, it has always said this right should be respected.
Furthermore, a new opposition party, the Tigray Independence Party (TIP), has emerged to contest the regional election. It describes Ethiopia as an "empire", and says its prime mission is to secure Tigray's independence.
Some academics in Tigray are also entertaining the idea of secession. So for the first time since 1991, the topic is on the agenda of mainstream politics in Tigray.
Two other Tigray nationalist parties contesting the poll, Salsay Woyane Tigrai and Baytona, say they want the region to have more autonomy to secure its territorial integrity, promote its language, and preserve its heritage.
The TPLF currently controls all the seats in the regional parliament, and the election will be carefully watched to see if the more nationalist and pro-secession parties win some seats to pursue their agenda further.
As for Mr Abiy, he has repeatedly said that Ethiopia will "never" disintegrate, indicating that he is confident that he can hold the nation together, despite the ethnic, religious and political violence that has hit different parts of the country, leaving about two million people homeless since he took office.
The TPLF says the displaced include about 120,000 Tigrayans, who constitute, according to the 2007 census, around 6% of the population.
What about mediation efforts?
On 16 August, more than 50 religious leaders, elders and prominent personalities travelled from the federal capital, Addis Ababa, to Mekelle city in an attempt to ease tensions. The fruit of their efforts are yet to be seen.
The ICG think-tank said "weightier" mediators may be needed.
"Prominent African statesmen with strong ties to both the TPLF and Abiy could play this role," it added.
Other analysts say this is vital as the success of Ethiopia's peace initiative with Eritrea hinges on stability in Tigray.
The region borders Eritrea, and was at the centre of the 1998 war between the two nations.
Tens of thousands were killed in the conflict after Eritrea launched an offensive to gain control of the town of Badme from Ethiopia's Tigray region.
Mr Abiy signed a deal in 2018 with Eritrea's President Isaias Afwerki to end the "state of war", resulting in border crossings between the two countries reopening.
However, the border crossings are once again shut. The reasons are unclear, but the Ethiopian government at one point said that the two countries were working to establish proper customs posts. Nor has the status of Badme been resolved. Eritrea wants Ethiopia to abide by a UN-backed border commission ruling to hand over the town. But this cannot be achieved without the cooperation of the government in Tigray, as it administers the area. So, the Nobel laureate may find that to achieve lasting peace with Eritrea, he will first need to resolve his differences with the TPLF.