Thein Sein, a former general who has won international praise for dramatic reforms since he became president in 2011, said lively debate about revising the charter showed increasing "political maturity".
"I believe that a healthy constitution must be amended from time to time to address the national, economic, and social needs of our society," he said in a speech published in the English-language New Light of Myanmar newspaper.
He said he supported amending provisions which exclude anyone whose spouse or children are overseas citizens from becoming president - a clause widely believed to be targeted at Suu Kyi whose two sons are British.
Suu Kyi has vociferously campaigned for a change to the 2008 constitution, which also ring-fences a quarter of the seats in parliament for unelected military personnel.
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The charter change issue is rising to the fore as Myanmar prepares for key 2015 parliamentary elections, seen as a definitive test of whether the military is willing to loosen its grip on power.
The country's president is selected by the legislature.
On Saturday Suu Kyi's opposition National League for Democracy (NLD) party said it would not boycott the 2015 poll, even without a constitutional amendment first to allow her to become president.
Since then Thein Sein has pushed through sweeping changes, including welcoming Suu Kyi and her party into parliament following landmark by-elections in 2012.
In his speech Myanmar's leader said he had "tried to promote harmony" while in power, but warned that the country risked a political impasse if the demands of the people "are larger than what the current political system can accommodate".
"If this happens, we could lose all the political freedom we have achieved so far," he said.