Relations between the armed forces and Suu Kyi will define the success of Myanmar's emergence from decades of isolation and military rule that began when the army seized power in 1962.
"We don't have any reason to reject the leadership of the elected civilian government," Senior General Min Aung Hlaing said at a rare news conference at the military headquarters on the outskirts of the capital, Naypyitaw.
The army is the most powerful institution in the Southeast Asian country.
It ruled directly for nearly 50 years, but handed over power to a government led by retired officers in 2011 which organised an election in November last year.
Suu Kyi's party won by a landslide after years of opposition to military rule.
A government controlled by Suu Kyi took over in April after a transition dominated by discussion over the army-drafted constitution, which bars Suu Kyi from the presidency.
The military maintains a significant political role with control of three security ministries. It also holds a quarter of seats in parliament which gives it a veto on changes to the constitution.
In the first week of her administration, military lawmakers made clear their opposition to a bill creating a position of state counselor - a powerful advisory role for Suu Kyi - by refusing to participate in a vote on it.
But on Friday, Min Aung Hlaing struck a conciliatory tone.
"We're carrying out our duties under the leadership of the government. This is in accord with constitutional provisions," he said when asked about the relationship between the military and Suu Kyi's National League for Democracy.
He said the army reported important matters to President Htin Kyaw, who is a Suu Kyi loyalist hand-picked by her, and, when necessary, to Suu Kyi as well.
He said the military had to seek the approval of the president when it came to certain budget matters.
The 2008 military-drafted charter bars Suu Kyi from becoming president because her children are not Myanmar citizens. Her late husband was a British academic.
She is state counselor and foreign minister.