Remains of 12,000 soldiers still missing on Iwo To, also known as Iwo Jima, after 1945 battle with the US

The Japanese prime minister, Naoto Kan, has vowed to find the remains of about 12,000 soldiers still missing on Iwo To (also known as Iwo Jima) more than 65 years after the island was the scene of one of the most deadly battles of the second world war.

Speaking at a ceremony in Tokyo to inter the remains of 882 people found on the island last year, Kan said the authorities would locate the missing men as soon as possible.

"Many fallen soldiers remain," he said. "We vow to find them as soon as possible. We will do all we can to organise searches for them."

The US marines' assault on Iwo To on 19 February 1945 marked the start of a fierce battle in which 21,570 Japanese soldiers – almost the entire military contingent on the island – and 6,821 American soldiers died. The 36-day campaign is the most costly battle in the history of the US marine corps.

Dozens of remains are uncovered every year on Iwo To, a volcanic island 700 miles south of Tokyo, but an estimated 12,000 Japanese and 218 Americans are still classified as missing in action there.

Kan made the recovery of soldiers' remains a priority when he became prime minister last June; in December he became only the second Japanese leader to visit the island, now home to a self-defence force base.

Male members of the prewar civilian population were drafted into military service, while others were ordered off the island and have never been allowed to return permanently.

Kan said during his visit that the government was responsible for uniting the missing remains with their families. "I promise to repatriate as many soldiers as possible by sifting through each and every grain of sand," he said.

He was partly inspired by Clint Eastwood's 2006 films about the battle, Flags of Our Fathers and Letters from Iwo Jima, which told the story of the battle from both sides.

The latest civilian-led recovery effort began last summer and was boosted by the discovery in October of two mass graves thought to contain the remains of up to 2,200 Japanese soldiers.

In all, the remains of an estimated 1.1 million Japanese who died on Iwo To, Okinawa and overseas locations in wartime have yet to be recovered.

The island's peak, Mount Suribachi, is perhaps best known as the location of Joe Rosenthal's photograph of six US servicemen raising the stars and stripes on 23 February 1945 – the second flag raised that day.

The US invasion of Iwo Jima – which reverted to its prewar name Io To in 2007, is regarded as a major turning point in the Pacific war.

The island was home to an early warning radar station, and airfields that the US needed as a base for aeroplanes sent to escort larger aircraft during bombing raids on Tokyo and other Japanese cities.

The task of finding the remains has been complicated by the huge network of tunnels, caves and bunkers in which Japanese soldiers waited for the US invasion forces. Few Japanese soldiers wore dog tags or other forms of identification.

Iwo To remained under the control of the US military until it was returned to Japan in 1968.