Myanmar's president has joined the army chief in congratulating Aung San Suu Kyi's opposition after it swept national elections, and promised a smooth transition of power.

The country has been dominated by the military for half a century through direct junta rule and, since 2011, a quasi-civilian government run by its allies.

But Suu Kyi's National League for Democracy (NLD) is on the verge of tipping the balance of power after capturing more than 85 percent of seats declared so far from Sunday's election -- a huge stride in its long democracy struggle.

In a statement on Facebook Wednesday President Thein Sein, whose government has steered recent reforms, said "we would like to congratulate" Suu Kyi for "winning the people's approval."

"As the government, we will respect and obey the election results and transfer power peacefully."

The NLD has swept up 256 seats, just over 70 short of an outright majority. But it was almost certain to smash through that marker, with more official results due to be released on Thursday.

Suu Kyi on Wednesday called for national reconciliation talks with the powerful army chief Min Aung Hlaing and Thein Sein, stressing the need for a peaceful transition.

Both men agreed to discussions after the Union Election Commission announces the full results, with the army chief also taking to Facebook to congratulate Suu Kyi on "winning a majority."

Lower house speaker Shwe Mann, a former general once tipped as a possible compromise candidate for the presidency, also accepted the invitation to talk.

Their comments may go some way to allaying the fears of many NLD supporters who remain deeply suspicious of the army and its political allies, after past crackdowns on democracy movements that have left hundreds dead and thousands jailed .

Suu Kyi's party won a 1990 election by a landslide only for the army to ignore the result and tighten its grip on power.

Her path to power is blocked by an army-scripted 2008 constitution that bars anyone with foreign children -- or husband -- from the presidency.

Her sons are British as was her late husband -- who died in Britain while she was under house arrest in Myanmar.

The army is also gifted 25 percent of parliamentary seats uncontested, as well as control of Myanmar's security apparatus -- meaning it will retain immense power despite the huge support for the NLD.