The Southeast Asian nation was dominated by the military for more than half a century until Wednesday when Suu Kyi and her pro-democracy party took power.
The Nobel laureate, whose party secured a landslide election win in November, has vowed to rule the country despite a constitutional block on her becoming president.
In a surprise early act of parliamentary business by the new government, Suu Kyi's party proposed a bill to grant her a special "state counsellor" position.
In a sign of early turbulence between her party and the still hugely influential army, military MPs called the move unconstitutional in an upper house debate today that saw the bill pass its first legislative hurdle.
Colonel Myint Swe raised fears the plan would place the "president and the advisor at the same level".
"This is in opposition to the constitution. So I would like to suggest the bill be amended according to the constitution," he told lawmakers.
The army is reserved a quarter of all parliamentary seats by a charter they scripted.
The NLD's huge election win gave it a sweeping majority in the legislature, so the bill passed a vote in the upper house, but still needs to be approved in the lower house and combined parliament.
Suu Kyi is the head of the National League for Democracy party and the figurehead of its near 30-year struggle to end military domination.
She has pledged to rule through her longtime friend and confidante Htin Kyaw, who was sworn in as president Wednesday.
But observers have raised concerns over how her novice government will tackle mammoth challenges in a nation scarred by decades of repressive and economically-destructive army rule.
Suu Kyi is taking on a huge workload in the new administration, running the ministries of foreign affairs, education, energy and the president's office.
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