The disaster could have been caused by undersea landslides from the eruption of Anak Krakatau, a volcanic island formed over years from the nearby Krakatau volcano, scientists from Indonesia's Meteorology and Geophysics Agency said.
After raising the volcano's alert level on Thursday, authorities went on to impose a five-kilometer exclusion zone.
With Anak Krakatoa still rumbling amid high-tide warnings, many survivors who have been evacuated to higher ground are too afraid to return home, saying they are anxious that another tsunami will strike.
The new flows posed no immediate danger to towns as the volcano sits in the middle of the Sunda Strait between Java and Sumatra islands.
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As The Associated Press notes, "The disaster struck without warning, taking people by surprise in a country that regularly suffers landslides, earthquakes and volcanic eruptions".
A crater collapse on Anak Krakatoa at high tide on Saturday night is thought to have sent waves smashing into the Indonesian shoreline, engulfing fishing villages and popular resorts along the coasts of western Java and south Sumatra.
Disaster agency spokesman Sutopo Purwo Nugroho said on Monday: "The lack of a tsunami early warning system caused a lot of victims because people did not have the time to evacuate".
Authorities say at least 479 people have died and hundreds more are missing.
"Today we're focusing on helping the evacuees in shelters by setting up public kitchens and distributing logistics and more tents in suitable places", he told AFP on Tuesday.
Indonesia has widened the no-go zone around an island volcano that triggered a tsunami on the weekend, killing at least 430 people in Sumatra and Java. Some residents defied the warning, returning to what was left of their homes to begin cleaning up as heavy rain fell and waves pounded the shore.
Karnawati said the tsunami was probably caused by the collapse of a big section of the volcano's slope.
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Thick ash clouds continued to spew from the mountain, and authorities and experts have warned of further high waves and advised residents to stay away from the shoreline.
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Radar data from satellites, converted into images, shows Anak Krakatau shrunk dramatically following Saturday's eruption.
It was the second tsunami to hit Indonesia in the past three months.
The vast archipelago nation is one of the most disaster-hit nations on Earth due to its position straddling the so-called Pacific Ring of Fire, where tectonic plates collide.
In September more than 2,000 people were killed and about 80,000 people displaced in Central Sulawesi after a devastating quake and tsunami struck the island.
Anak Krakatoa, which means child of Krakatoa, is the offspring of the infamous Krakatoa volcano that affected global climate with a massive eruption in 1883.
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