"The next few months will be crucial for the country's future," she said.
The constitution was crafted under the former military regime and blocks anyone, like Suu Kyi, whose spouses or children are foreign nationals from leading the country.
"If the government does not support moves to amend the constitution then we can conclude that the government is not interested in genuine democracy," Suu Kyi, who has said she will run for president at elections in 2015, told reporters.
Answering a question from a reporter who asked if boycotting the elections was an option, Suu Kyi said "we believe in keeping doors open for as long as possible."
Suu Kyi, 68, was speaking after meetings with Hungarian President Janos Ader and Deputy Foreign Minister Zsolt Nemeth.
Suu Kyi spent 15 years under house arrest under military rule in Myanmar, before she was freed after controversial elections in 2010.
The democracy icon is now an opposition lawmaker as part of sweeping reforms under a new quasi-civilian regime that took office in 2011.
She arrived in Hungary from Poland and travels Saturday to the Czech Republic.