Suu Kyi's party has refused to swear to "safeguard" an army-created constitution in the first sign of tension with the government since a landmark by-election this month saw the democracy icon win a parliamentary seat.
The spat comes as European Union nations put a halt to most sanctions against the impoverished nation for one year to reward a series of dramatic reforms since direct army rule ended last year.
Foreign ministers from the 27-nation bloc agreed a one-year suspension of measures against almost 500 individuals and more than 800 firms in a meeting in Luxembourg on Monday, diplomats told AFP.
"As a means to welcome and encourage the reform process, the Council will suspend restrictive measures imposed on the government, with the exception of the arms embargo, which it will retain," said a statement adopted by the ministers.
Myanmar, long-isolated under military dictatorship, has seen a rapid improvement in relations with the international community after the Nobel Peace Prize winner and her party achieved a decisive win in the April 1 polls.
Suu Kyi has shown increased confidence in the reformist government of President Thein Sein in recent weeks, calling for the EU sanctions suspension and planning her first international trip in 24 years.
Thein Sein, who is currently on a visit to Japan, on Monday vowed that he would not backtrack on the country's democratisation.
"There won't be any U-turn," Thein Sein said, according to the Mainichi Shimbun.
He told reporters that it was up to Suu Kyi whether or not she took her seat in parliament.
Suu Kyi's National League for Democracy (NLD) -- the main opposition force after securing 43 of the 44 seats it contested in the by-elections -- has appealed to the president directly over the stalemate, asking that the wording of the oath be changed from "safeguard" to "respect" the constitution.
The NLD, which boycotted a controversial 2010 election, agreed to rejoin the political mainstream last year after authorities changed a similar phrase in party registration laws.
Suu Kyi has said one of her priorities as a politician is to push for an amendment of the 2008 constitution, under which one quarter of the seats in parliament are reserved for unelected military officials.
MPs from other parties took the oath in a new session of parliament on Monday.
Myanmar analyst Aung Thu Nyein, of the Thailand-based Vahu Development Institute, said the NLD had "made the wrong move" in making a stand over the oath.
"I think the NLD should participate in the parliament and then they should propose comprehensive political and economic reform strategies," he said, adding that the wording appears in the constitution itself and the president is therefore unable to change it.
Myanmar's new regime has freed hundreds of political prisoners and signed tentative peace deals with a number of rebel groups as part of its reform programme, although fighting continues in the far north.
The international community has begun easing sanctions as it looks to balance fears over the sustainability of the changes and a desire to bolster regime reformers who may face pressure from those wary of change.
The EU decision, which comes after more tentative moves from the United States, could open up the resource-rich Southeast Asian nation to European firms.
The bloc "will monitor closely the situation on the ground, keep its measures under constant review and respond positively to progress on ongoing reforms," the EU statement added.
European visa bans on 87 top Myanmar officials, including President Thein Sein were lifted in February.