Heavy rain was lashing the area around Kumamoto, where officials warned quake-loosened hillsides could be at risk of collapse as aftershocks continued to roil the ground.
"The wind is expected to pick up and rain will likely get heavier," Prime Minister Shinzo Abe said.
"Rescue operations at night will be extremely difficult ... It's a race against time."
Isolated villages in mountainous areas near the city of Kumamoto were completely cut off by landslides and damage to roads. At least 500 people were believed trapped in one settlement.
A 7.3-magnitude tremor struck early on Saturday morning, injuring about 1,000 people and causing widespread damage to houses, roads and bridges.
It was the second major quake to hit Kumamoto province on the island of Kyushu in just over 24 hours. The first, late on Thursday, killed nine people.
Around 400 aftershocks of at least level 1 on the Japanese scale have occurred since Thursday's shock, broadcaster NHK reported.
Television footage throughout Saturday showed fires, power outages, collapsed bridges, a severed road hanging over a ravine and gaping holes in the earth.
More than 90,000 evacuated
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