The warning came as the nation marked the anniversary of the 2004 tsunami in which 130,000 Indonesians died - majority in Aceh - after a magnitude 9.1 quake in the Indian Ocean spawned giant walls of water that killed 230,000 across 14 countries.
The eruption came at high tide during a full moon, with the Sunda Strait also experiencing a spell of high rainfall, government and rescue agencies said.
At least 430 people were killed, with 1,495 people injured and another 159 were missing.
Heavy rains and high seas have hampered the search effort.
She said the tsunami was probably caused by the collapse of a big section of the volcano's slope. Sunday's event, coupled with an quake and tsunami in September on Indonesia's Sulawesi island that killed at least 2,100 people, triggered flashbacks for some who survived the 2004 tragedy.
The tsunami on Saturday roared ashore with little warning, officials said, acknowledging that no alert had been sounded in advance because the nation's warning system detects only tsunamis spawned by temblors.
"I'm here because people said there could another tsunami", Etin Supriatin said from an evacuation center in shattered Labuan.
A boat is seen ashore in Teluk village Labuan subdistrict in Banten province on the west coast of Java island
Authorities also widened a no-go zone around Anak Krakatau to 5km (three miles) - up from a previous 2km - and warned shell-shocked residents to stay away from the coast, after more than 400 were killed by Saturday night's killer wave.
The death toll from the tsunami triggered by a volcanic eruption in Sunda Strait of western Indonesia has climbed to 429 so far, with a total of 1,459 others injured, a spokesman of the national disaster agency said on Tuesday.
The agency was monitoring Anak Krakatau's eruptions as stormy weather and high surf continued to plague the area, said agency head Dwikorita Karnawati. That was caused by a magnitude-9.1 natural disaster off the northern.
It is the product of the infamous Krakatau, whose tsunami-triggering eruption in 1883 was one of the largest of modern times, killing more than 36,000 people and leaving a massive crater in which grew Mt. Anak Krakatau, or "Child of Krakatau".
"Seconds later I saw people running from the tsunami wave shouting 'Tsunami!" That was preceded by a series of deadly earthquakes early this year that rattled the popular tourist destination of Lombok island, near Bali.
Indonesia President Joko Widodo vowed to have tsunami-detection equipment repaired or replaced, after his own officials complained that a system of warning buoys - set up after the calamitous Indian Ocean tsunami of 2004 - had not been functioning for years. "I didn't get information from anywhere", he said, adding there had been little help for residents since disaster struck.
The vast archipelago, which sits in the Ring of Fire, which runs around the Pacific basin, has suffered its worst annual death toll from disasters in more than a decade.
"We're scared of the sea".
Italy's Mount Etna erupts, authorities close airport
The Etna observatory reported lava flows from the volcano and said a new fracture had opened near its southeast crater. Flights were restricted to just four landings an hour at the nearby airport at Catania because of poor visibility.