Speaker Shwe Mann walks ahead of commander-in-chief Ming Aung Hlaing and Aung San Suu Kyi at the Presidential palace in Naypyitaw on April 10, 2015. Suu Kyi has reached out to them and President Thein Sein as her party heads for a win in elections held on Sunday. Reuters

Aung San Suu Kyi has asked to meet with Myanmar's military-backed rulers, whom she is poised to share power with as her party racks up seats from Sunday's parliamentary election.

“Implementing the people’s desires calmly after Election Day is very important for the country’s dignity, and for our people’s peace of mind,” the Wall Street Journal reported Suu Kyi as saying in letters to Min Aung Hlaing, who heads the military, Myanmar President Thein Sein and speaker of parliament Shwe Mann.

“I would like to invite you to discuss reconciliation next week at a time of your convenience," The Guardian reported her saying.

Shwe Mann, who has been saying he would work with Suu Kyi, said he already accepted the invitation to talk, the Journal reported. He lost his seat in Sunday's election.

Suu Kyi's National League for Democracy has won 163 of lower house seats declared as of Wednesday morning, compared with just 10 seats for the ruling Union Solidarity and Development Party. At that rate, she will probably get a majority despite the military's right to fill 25 percent of the parliament, the Journal said. Still, she needs to deal well with the military and its allies because -- aside from those parliamentary seats -- they will retain control of three key departments: Defense, Home and Border Security, according to the New York Times.

The Home Ministry controls the police and the whole bureaucracy, which is staffed by many former military officials, the Times said.

“This was not an election of a government,” the Times quoted Thant Myint-U, a historian and sometime government adviser, as saying. “It was an election for a spot in a shared government with the army.”

The parliament will elect a president by March next year. Suu Kyi, who retained her own seat in Kawmhu, Yangon, isn't eligible because of a law that bars people who are married to or closely related to foreigners. Suu Kyi's late husband was British, as are their two sons. She says she will rule as party leader above the president, whom she will choose.

If there is a peaceful turnover, Myanmar will have its most democratic government since 1962, when the military staged a coup. In 1990, the military called an election that Suu Kyi and her allies won. But the military then refused to hand over power, putting Suu Kyi under house arrest instead for most of the next 20 years. Under house arrest, she won the Nobel Peace Prize and became known as an "icon of democracy."