Survivors evacuated to the Yemeni port city of Hodeida said four of the soldiers were killed outright when the volcano erupted on the island of Jabal al-Tair, some 150 kilometres (90 miles) away.
"Four of our comrades have died, burned by the lava," said one soldier who was among the evacuees.
"They were killed immediately after the eruption of the volcano at 5:30 pm (1330 GMT) on Sunday," another soldier told AFP.
The bodies of two other soldiers were recovered from the sea by a Canadian navy frigate which joined a search and rescue effort to find eight people listed as missing after the eruption, following a request by the Yemeni coastguard.
The frigate, HMCS Toronto, was passing through the Red Sea along with several other NATO warships steaming north to the Suez Canal when it received the request for assistance, the navy said.
Two other soldiers were rescued from the sea by small boats dispatched from the frigate, and Yemeni authorities said the six killed and two rescued accounted for the eight people earlier listed as missing.
An AFP correspondent in Hodeida said 15 soldiers among the 49 evacuated from the island had been injured, most with injuries to their legs.
Yemeni President Ali Abdallah Saleh flew over the zone in a helicopter on Monday to assess the damage, the Saba news agency said.
Infra-red pictures taken from the deck of the Toronto show lava and ash spewing from the volcano on the centre of the four square-kilometre (1.54 square mile) island.
There had been considerable seismic activity around the island ahead of the eruption, the Yemeni defence ministry said on its website. It said that an earthquake measuring 7.3 on the Richter scale had been recorded on Friday.
Comment: There was a lot of seismic activity as can be seen here, but the 7.3 appears to be an error, as it has not been corroborated elsewhere.
The 1,200 metre-high (3,937 feet) volcano last erupted in the 19th century, Saba quoted geologists as saying.
"It was extremely brilliant...," Ken Allen, a Canadian Navy spokesman onboard the Toronto told CNN.
"The closer we got to the area, the brighter it got. We could actually see the lava spouting... up into the sky", he said.
Saba reported that "all necessary measures have been taken to ... follow the course of the eruption," adding that a team of volcanologists had been dispatched to the area.
The island has been garrisoned by the Yemeni authorities since the 1990s when a longstanding territorial dispute with Eritrea over the ownership of a series of islands in the Red Sea erupted into armed clashes.
The Permanent Court of Arbritration in The Hague eventually found in Yemen's favour and awarded it sovereignty over the islands.
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