Suu Kyi's National League for Democracy said it received a message from Information Minister Ye Htut on behalf of President Thein Sein congratulating it for leading the race for parliamentary seats in Sunday's election.
Ye Htut said the government will pursue a peaceful transfer of power "in accordance with the legislated timeline." He was not immediately available for comment.
The message helps remove lingering concerns that the military, which has a large influence over the ruling party, may deny the NLD power, as it did after elections in 1990.
But while an NLD victory virtually assures it of being able to elect the president as well, Suu Kyi remains barred from becoming president by a constitutional provision inserted by the military before it transferred power to a quasi- civilian government in 2011.
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Suu Kyi has declared, however, that she will become the country's de facto leader, acting "above the president," if her party forms the next government.
She described that plan further in interview yesterday with Singapore's Channel NewsAsia television.
The military, which took power in a 1962 coup and brutally suppressed several pro-democracy uprisings during its rule, gave way to a nominally civilian elected government in 2011 - with strings attached.
It installed retired senior officers in the ruling party to fill Cabinet posts and gave itself key powers in the constitution, including control of powerful ministries and a quarter of the seats in the 664-member two-chamber Parliament.
While Myanmar's people voted overwhelmingly Sunday to remove the military-backed Union Solidarity and Development Party from power, it's clear that the army's involvement in politics won't end, and the NLD will need to convince it to cooperate.