A Japanese naval destroyer equipped with sophisticated radar key to the country's missile defence system collided with a fishing boat on Tuesday, the coastguard said, raising questions about the ship's monitoring.

Two men on board the 12-metre (39 ft) fishing boat were missing after the collision east of Tokyo, prompting a search by military and coastguard vessels and aircraft.

The Atago destroyer, commissioned last spring, is the newest of Japan's five ships equipped with high-tech Aegis radar systems and typically carries a crew of around 300.

The opposition Democratic Party's top point person on defence said the party wanted an explanation of the incident from authorities, including why the destroyer's crew and defensive radar had not seen the fishing boat.

"This radar system should be better than any other ship's," lawmaker Keiichiro Asao told Reuters. "If they were not aware of the fishing boat, they could be attacked by any terrorists."

Some analysts said the Aegis system, used primarily for air defence, was unlikely to have been at fault.

"This would appear to be human error - an oversight or a procedural mistake," said Lance Gatling, CEO of aerospace consultancy Gatling Associates, in an email interview.

Incidents involving the military are sensitive in Japan, where a streak of pacificism runs deep and the post-World War Two constitution bans the maintenance of armed forces. The ban has been interpreted as allowing a military for self-defence.

TV pictures showed divers searching for the missing crew as the bright red and white prow of the fishing boat, which was split in half in the collision, bobbed up and down in the waves surrounded by fishing floats and other debris.

A group of about 80 people beating drums and gongs gathered to pray on the dock where Haruo Kichisei, 58, and his 23-year-old son Tetsuhiro had set out on a tuna fishing trip early Tuesday.

The incident comes as Prime Minister Yasuo Fukuda's popularity is slipping due to doubts about his leadership.

A survey by the conservative Yomiuri newspaper published on Tuesday showed support for Fukuda's cabinet had fallen to 39 percent, with a disapproval rating of 51 percent.

Japan's missile defence system, introduced with U.S. help after North Korea fired a missile over Japan in 1998, has Aegis ship-based SM-3 missiles and land-based PAC-3 interceptors.

The Atago was heading back to Japan after a training exercise in Hawaii, a defence ministry spokesman said.

A similar Japanese ship equipped with SM-3 missile defence equipment successfully shot down a dummy ballistic missile off Hawaii in December in a joint exercise with the United States.

The Aegis radar system, supplied by Lockheed Martin Corp, is used by the U.S. Navy and other naval forces around the world.