In the upcoming upper house elections the hawkish Abe is aiming to secure a two-thirds majority for his Liberal Democratic Party in combination with coalition allies and supporters so that he can alter the charter.
Analysts said the lower house by-election on the northern island of Hokkaido was a test for Abe's national security agenda, including new laws that took effect last month.
Under that legislation the military, known as the Self-Defence Forces, could under certain conditions go into battle abroad to protect allies.
The LDP and allies already have a two-thirds majority in the more powerful lower house, where elections are not due until late 2018, unless Abe chooses to dissolve the chamber before then.
But constitutional revision requires two-thirds majorities in both houses and the support of a majority in a national referendum.
LDP candidate Yoshiaki Wada won the Hokkaido by-election in a tight race against an independent backed by opposition parties, according to exit poll projections by public broadcaster NHK and Jiji Press.
Abe welcomed the result as a "big" win ahead of the summer vote, Jiji reported.
In the day's other lower house by-election in Kyoto prefecture in western Japan, Kenta Izumi of the opposition Democratic Party was tipped as the winner.
That election was held to fill the seat of an LDP lawmaker who resigned in disgrace earlier this year after he admitted cheating on his wife, also a member of parliament.
The LDP refrained from fielding a candidate in the vote.
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