The landslide hit Pasir Langu village in Bandung Barat region early on Saturday and was triggered by heavy rains starting a day earlier.
The village was located in a hilly area of the province about 100km southeast of Indonesia's capital, Jakarta.
The 23 Marines were caught in the landslide during training exercises for Indonesia-Papua New Guinea border patrols on Saturday, First Admiral Tunggul, the Navy spokesperson said.
"The incident occurred due to extreme weather conditions with heavy rainfall, which caused a landslide at the training site," said Tunggul, who goes by only one name.
As of Tuesday afternoon, the death toll from the landslides had risen to 20 from the previous 17, with 42 people still missing, said Abdul Muhari, a spokesperson at Indonesia's disaster mitigation agency.
It was not immediately clear if the soldiers were included in those declared dead by the agency.
At least 800 rescuers, military and police personnel along with nine excavators have been deployed to find the missing people.
Muhari said 685 residents of the stricken village had been evacuated to local government buildings.
The landslide happened during the peak of the wet season on Java island. Floods hit several parts of Indonesia last week, including Jakarta and some cities in West Java and Central Java.
The landslide occurred two months after cyclone-induced floods and landslides on the island of Sumatra killed 1200 people, destroyed homes and displaced over a million residents.
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