Uncertainty surrounds the handover of power in the Southeast Asian nation, after Suu Kyi's opposition National League for Democracy swept to victory in the November 8 polls, the fairest elections in 25 years.
She held a closed-door meeting in the capital Naypyidaw with Shwe Mann, a former general with whom she has an amicable working relationship.
The pair agreed to a number of shared goals that were later released in a statement by the NLD, including national reconciliation, peace and the smooth running of parliament during the country's political transition.
Suu Kyi has requested three "national reconciliation" discussions, including with the president and army chief.
Shwe Mann had at one point been tipped as a potential compromise candidate for the role.
But he was ousted from the leadership of the army-backed ruling Union Solidarity and Development Party in August, and then lost his constituency seat in the elections.
But he continues to wield influence as speaker of the combined national parliament, which reconvened this week for a lame duck session that will last until January.
There are jitters over Myanmar's transition, specifically who will be the next president -- a role denied to Suu Kyi by the army-drafted constitution because she married and had children with a foreigner.
Suu Kyi has requested talks with President Thein Sein and powerful army chief Min Aung Hlaing to try and smooth a change of leadership that will further chip away at the military's influence.
Both men have agreed to the meetings and congratulated Suu Kyi on her party's poll victory.
This has jarred nerves in Myanmar, where the NLD's 1990 electoral landslide was ignored by the then ruling junta, who held onto power for a further two decades before ceding to a quasi-civilian regime in 2011.
Thein Sein will remain in office until March under Myanmar's complex system, which enshrines a lengthy power handover as well as continued political and economic clout for the military.
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