Correspondents say air quality has improved across Java, but cities and villages are still covered in a layer of dust and ash.
Tens of thousands remain in shelters, facing medicine and blanket shortages.
Mount Kelud, in Java's east, spewed ash and debris over a large area on Friday, killing three people.
The volcano had been rumbling for several weeks before it erupted.
Authorities said they were not expecting another major tremor, because the patterns showed volcanoes tended to quieten down after a large eruption.
The transport ministry said airports in Malang, Cilacap and Semarang reopened on Saturday.
"We are now evaluating the status of other airports," spokesman Bambang Ervan said.
The airports shut down because of low visibility. There were also fears that debris could damage aircraft engines.
Some 75,000 people are estimated to have sought refuge in temporary shelters.
Many are unable to return to their homes because authorities have kept a 10km exclusion zone in place around the volcano.
Local reporters say the volcano alert remains at the highest level because officials do not want to take any chances.
Officials raised an alert on Thursday about an hour before the volcano erupted.
They urged people living in 36 villages within 10km of the volcano to evacuate.
Officials said two people died when their homes caved in under the weight of gravel and ash.
A 70-year-old man was killed when a wall collapsed while he was waiting to be evacuated.
Some of the evacuees tried to return to their houses on Friday morning to gather their possessions, but were forced to turn back by the stream of volcanic ash and rocks from the volcano.
Indonesia lies on the Ring of Fire, a series of geological fault-lines, prone to frequent earthquakes and volcanic eruptions.
There are about 130 active volcanoes in Indonesia.
Earlier this month, Mount Sinabung on the island of Sumatra erupted, killing at least 14 people and making many homeless.
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