Opposition members of parliament and democracy activists have raised fears military lawmakers, who have 25 percent of seats guaranteed under the current constitution, may prove an obstacle to amending the document regardless of whether the government presses for change.
But former general-turned-speaker Shwe Mann on today told reporters that the decision to amend the constitution -- or not -- before a hotly-anticipated general election in 2015 will need the blessing of reformist President Thein Sein's government.
"How far we can complete an amendment of the constitution (before 2015) depends on the struggle between committee members," Shwe Mann, who is chairman of both lower and upper houses, told reporters in a rare press briefing convened in the capital Naypyidaw.
"The main thing is that it's very important the administration is involved. Whenever a law is enacted, the involvement of the administrative body is very important."
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A major hurdle to Suu Kyi's stated presidential ambitions is the current constitution, crafted under the former military regime and which blocks anyone whose spouses or children are overseas citizens from leading the country.
Opposition politicians and democracy activists have criticised the constitution, which was written by the former junta more than a decade ago and approved by a nationwide referendum in 2008 soon after the country had been battered by a cyclone.
Shwe Mann said any tweaks to the constitution must be done "very carefully" but insisted the issue was being taken seriously within parliament.
But one lower house lawmaker told AFP the government will be instrumental in the path ahead for any amendment.
"Without the cooperation of the executive we can not do it," the MP added, requesting anonymity.
Suu Kyi in June said she wanted to run for the top office.