Malaysian officials said the death toll from the earthquake that struck on Friday morning had risen to 16, with three more bodies recovered.
Three more people remain missing.
The Singaporean students were part of a school excursion to the popular climbing destination, which was jolted by a 6.0-magnitude quake just as the 4,095-metre-high (13,435-foot) peak was crowded with hikers.
The tremor triggered thunderous landslides that obliterated sections of trail on the mountain, located in the state of Sabah on Borneo island.
Malaysian officials have so far released few details on the identities of the victims, but Singapore's Education Ministry confirmed the deaths of the 12- and 13-year-old students and one teacher.
"We are deeply saddened to inform that the bodies recovered by the Malaysian authorities have been identified by their next-of-kin as five students and one teacher from Tanjong Katong Primary School," it said in a statement.
It said a Singaporean adventure guide who accompanied the school group also died and that one other student and a teacher remained missing.
Masidi Manjun, tourism minister for Sabah state, said on Twitter that search teams were focusing on a section of the mountain where he said a "river of stones" had left a major trail impassable.
Mohammad Farhan Lee Abdullah, police chief of the town of Ranau near the mountain, said that body parts had been found on sections of the mountain, suggesting the awesome power of the landslides.
It was not immediately clear whether the body parts were from corpses already found or were from the three still missing.
"They are in parts probably because of rocks and boulders falling on them but we need to do forensics first," Mohammad Farhan said.
The local Kinabalu Today news portal quoted rescue personnel saying that full recovery of remains could be impossible as some were pinned under massive boulders or possibly swept to their deaths from the peak.
Singapore's Straits Times newspaper said some of the Singaporean students were taking a route to summit that diagonally traverses a steeply sloping rock face and in which climbers are tethered to ropes attached to the surface.
The area is above the treeline and would have left those in that section exposed to the hail of stones and boulders.
- Aftershocks leave rescuers on edge -
Rescuers Saturday had escorted down to safety 137 hikers who were stuck on the mountain for up to 18 hours by the rockfalls.
Crews and officials engaged in search and rescue efforts have been kept on edge by aftershocks, including a Saturday afternoon temblor that Malaysian officials rated at 4.5-magnitude.
More tremors were felt in the area Sunday.
The quake, whose epicentre was near the picturesque mountain, was one of Malaysia's strongest in decades.
There have been no reports of major damage or any casualties outside of those at Mount Kinabalu.
Climbing has been suspended for at least three weeks so authorities can make repairs and assess safety risks.
Around 20,000 people complete the relatively easy climb each year.
Mount Kinabalu is sacred to the local Kadazan Dusun tribe.
Malaysian social media users and some officials have suggested the quake was a sign tribal spirits were angry after a group of 10 apparently Western men and women tourists last weekend snapped nude photos at the summit and posted them on the Internet.