The comments carry significant weight coming from the from Commander-in-Chief Min Aung Hlaing, the head of a military that ruled the country for half a century with an iron fist and kept Suu Kyi under house arrest for 15 years.
Suu Kyi, whose National League for Democracy party were poised for a massive victory after a 25-year struggle, had earlier called for talks on "national reconciliation".
She sent letters to Min Aung Hlaing, President Thein Sein and parliamentary speaker Shwe Mann, urging them to recognise the popular mandate.
"We congratulate the NLD for winning a majority of seats," he said, adding he will meet Suu Kyi after the official results are declared by election authorities.
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As the announcement was made, the NLD seemed poised for a massive victory after a 25-year democracy struggle, and on the brink of a majority after taking more than 85 percent of the seats declared so far.
Although poll officials are yet to announce the NLD as winners, Myanmar's balance of power, dominated for half a century by the army and its allies, may finally be shifting.
Information Minister Ye Htut earlier also congratulated the NLD on its gains and vowed to "respect" the election outcome and "work peacefully in the transfer" of responsibilities to the winning party.
The NLD has scooped up 256 seats, 73 shy of an outright majority -- but it was almost certain to smash through that marker.
In her letters Suu Kyi said the "citizens have expressed their will in the election," following the NLD's blitz of the ruling party.
The document also blocks the 70-year-old Suu Kyi from becoming president despite her position as the democracy movement's magnetic force.