On Saturday huge waves crashed into coastal towns on the islands of Sumatra and Java, killing at least 281 people and injuring more than 1,000.
Around 12,000 residents have been moved to higher ground with a high-tide warning extended to Wednesday.
Anak Krakatau erupted again on Sunday, spewing ash and smoke.
It is thought volcanic activity set off undersea landslides which in turn generated the mega waves.
Sutopo Purwo Nugroho, the spokesman for the National Disaster Management Agency, said another tsunami was a possibility because of the continued volcanic eruptions of Anak Krakatau.
"Recommendations from [the] Meteorology, Climatology and Geophysical Agency are that people should not carry out activities on the beach and stay away from the coast for a while," he said.
He said there was no tsunami advance warning system the night of the disaster, adding that because of lack of funds, vandalism to the buoys and technical faults there had been no operational tsunami warning system since 2012.
President Joko Widodo visited the area on Monday and said an alert system was needed.
Images captured by the European Space Agency’s Sentinel-1 satellite showed a large portion of the southern flank of the volcano had slid off into the ocean, scientists said.
This meant no tsunami warning was triggered.
What's left behind is a wasteland of collapsed houses and hotels and muddy roads strewn with twisted metal and wood.
More than 600 homes, 60 shops and 420 boats were destroyed.
Thousands of displaced and grieving residents were searching for missing loved ones on Monday and trying to salvage whatever they could of their belongings.
Rescuers are today using heavy machinery and their bare hands to pick through debris in the hope of finding survivors.
Medics were sent in with the military, while groups of police and soldiers reached remote areas.
Among the people rescued was a five-year-old boy who had been trapped under rubble for hours north of Labuhan on the west coast of Java island.
The tsunami struck at 9.30pm local time on Saturday during a local holiday.
The killer waves destroyed hundreds of buildings, sweeping away cars and uprooting trees in several popular tourist destinations including the Tanjung Lesung beach resort, west Java.
Footage shared on social media showed a wave crashing into a tent in the resort, in which Indonesian rock band Seventeen was performing.
At least four band members and support crew were killed, lead singer Riefian "Ifan" Fajarsyah told followers in a poignant Instagram post.
The band's drummer was among the missing, as was his wife, Dylan Sahara.
KEEP OFF THE BEACHES
TOURISTS and locals have been warned to stay away from beaches amid fears of another tsunami hitting the coast.
Officials said that Indonesia’s early warning system only recorded tsunamis from earthquakes — not volcanoes.
National Disaster Management Agency spokesman Sutopo Purwo Nugroho said: “The potential for a fresh tsunami is still possible because the volcanic eruption continues to occur.
“The recommendations are that people should not carry out activities on the beach and stay away from the coast.”
Azki Kurniawan, 16, was part of a 30-strong group of students on work experience at the Patra Comfort Hotel when people suddenly burst into the lobby, yelling “sea water rising”.
The teenager ran towards his motorbike when a 1m-high wave hit him.
“I fell down [as] the water separated me from my bike. I was thrown into the fence of a building about 30m from the beach, and held onto the fence as strong as I could, trying to resist the water, which feels like it would drag be back into the sea.
“I cried in fear… I was afraid I would die.”
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Nurjana, 20, ran for half an hour to the mountains after the tsunami hit. Her beachside stall, where she sold snacks to tourists, was washed away.
"I opened the door straight away and saved myself. I jumped over the wall," she told Reuters.
"Everything is destroyed."
Yadi, a middle-aged fisherman who operates a fleet of six boats that were among dozens that sank or were dragged out to sea by the waves, said: "People said 'run, run a wave is coming!'. There were three waves in a row.
"There was a real panic. Many people were left behind," he said, adding that he and his family escaped by running to higher ground.
No foreigners are known to have been caught up in the disaster, according to reports.
The Foreign and Commonwealth Office (FCO) said: "The British Embassy is in contact the Indonesian authorities and is monitoring the situation closely."
It comes almost 14 years to the day since the Boxing Day 2004 tsunami killed 226,000 people in 13 countries, including more than 120,000 in Indonesia.
The death toll is expected to rise as 57 people were still missing on Monday.
The day the earth shook: The 1883 eruption of Krakatoa
The explosion of Krakatoa sent tsunamis with waves up to 135ft across the ocean – killing more than 30,000 people.
Thousands more were suffocated by hot ash raining from the sky.
The eruptions were equivalent to 200 megatons of TNT – about 13,000 times the nuclear yield of the bomb dropped on Hiroshima in 1945.
They were also heard thousands of miles away – and are believed to be the loudest noises ever experienced in human history.
World temperatures dropped by more than 1C the following year due to the ash clouds in the atmosphere blocking the sun.
The island that Krakatoa stood on virtually disappeared.
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