The voting to fill vacant parliamentary seats around Myanmar was seen as a test of the de facto leader's popularity after a bumpy first year in office.
Her National League for Democracy (NLD) stormed to power after dominating a historic 2015 poll that ended half a century of brutal military rule.
But disillusionment with her administration has grown in some circles as the young government has struggled to push through promised reforms.
The NLD's comfortable majority was not threatened by Saturday's by-elections, which were mostly held to fill a handful of offices emptied by politicians who took on ministerial posts.
But initial results on Sunday indicated a measure of discontent among ethnic minorities, who make up a third of the population and have long struggled under the rule of the Bamar majority to which Suu Kyi belongs.
The NLD fared well in its strongholds around the commercial capital Yangon and in central regions further north, holding on to seats in at least eight races, according to Union Election Commission Chairman Hla Thein.
But it suffered an embarrassing rout in southern Mon state, where the party lost a lower house seat to the military-backed Union Solidarity and Development Party (USDP). The NLD had comfortably won the seat when it trounced the USDP just a year ago.
The loss comes after the NLD sparked mass protests in Mon last month by naming a local bridge after Suu Kyi's father -- a move seen as emblematic of the Bamar elite's steamrolling of minority cultures.
Meanwhile election officials said ballots were still being counted in Rakhine and Shan states, two areas seething with ethnic strife.
In Rakhine the NLD faced a tough three-way race over a lower house seat with the USDP and the Arakan National Party.
The two NLD rival parties peddle pro-Buddhist and ultra-nationalist agendas that are likely to appeal to voters in a state where anti-Muslim sentiment runs high.
In restive northeastern Shan state, races were held after being cancelled in 2015 because of fighting between the army and ethnic insurgents.
The clashes have since moved further north but continue to thwart the NLD's efforts to bring peace to Myanmar's borderlands.
In a rare national address last week, Suu Kyi conceded that reforms have stalled in some areas.
But she asked for more time to reboot a country whose economic, political and cultural institutions were gutted under 50 years of cloistered junta rule.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)