Support fell 7 percentage points from last month to 25 percent in a poll by the Asahi Shimbun daily, continuing a slide from an initial high of around 70 percent when Hatoyama took office last September.
A separate poll by the Mainichi Shimbun daily showed support at 33 percent, down 10 points from March.
Hatoyama's Democratic Party took power for the first time last year after winning a general election by a landslide, but voter doubts have since grown over the premier's decision-making abilities on the economy and diplomacy.
Around half of voters in the Asahi poll said Hatoyama should resign if he fails to settle a feud with Washington over where to relocate a US military base on Japan's southern Okinawa islands by the end of May, as he has promised.
The percentage of voters who planned to vote for the Democrats in an upcoming election for parliament's upper house fell to 24 percent from 30 percent, the Asahi poll also showed, narrowing a gap with its main opposition rival.
The Democrats need to win an outright majority in the upper house election expected in July to break free of vocal coalition partners that have muddled policy-making as Japan tries to overcome deflation and cut huge public debt.
