Ko Ni was shot in the head in broad daylight outside Yangon's airport late last month while waiting for a taxi, in a crime that rocked the political establishment.
Suu Kyi's ruling National League for Democracy party branded the killing a political assassination and "terrorist act" against their policies.
Ko Ni was a vocal critic of the army's lingering grip on power under Myanmar's new elected government and an important advocate for the country's embattled Muslims.
He had reportedly been pushing for changes to the constitution that currently guarantees the military a quarter of parliamentary seats and bars Suu Kyi from the presidency.
The gunman, named as Kyi Lin, was arrested at the airport after also fatally shooting a taxi driver who tried to stop him escaping.
After a series of leaks and conflicting comments from police, state media confirmed days later they had also arrested "alleged conspirator" Aung Win Zaw in the southern state of Karen.
Myanmar's presidency said police and military intelligence are now hunting his brother, former Lieutenant Colonel Aung Win Khaing, who originally ordered the killing.
"According to interrogations of culprit Aung Win Zaw... his younger brother Aung Win Khaing asked him to assassinate U (honorific) Ko Ni in July 2016," the office said in a statement.
"Around August-September 2016, Kyi Lin went to him and asked for a job. He offered Kyi Lin 800 to 1,000 lakhs kyat (USD 58,000-USD 73,000) to kill Ko Ni."
Police have identified Aung Win Khaing from CCTV images at the airport, which show him asking for flight arrival times before Ko Ni was shot.