"It's usual that NLD members and supporters are happy at this moment," she said in a statement.
"But words, behaviour and actions that can harm and sadden other parties and people must be avoided completely. I would like all NLD members to ensure that the victory of the people is a dignified victory," she added.
Aung San Suu Kyi
If confirmed, the win would mark a dramatic reversal in the political fortunes of the veteran activist, who was locked up by the former junta for most of the past 22 years.
Official results were expected within a week. Observers says Myanmar's quasi-civilian government needs Suu Kyi to take a place in parliament to bolster the legitimacy of its political system and spur an easing of Western sanctions against the regime.
But even if her party were to win all 44 seats it contested in Sunday's by-elections, it would not tip the balance of power in a parliament dominated by the military and its political allies.