The spokesman said a border guard ship had taken aboard all 28 crew members from the trawler, identified as Albatros-101, which had refused orders to stop for its papers to be checked.
He said a coast guard aircraft had fired at the trawler during the pursuit, setting it ablaze and wounding an unknown number of crewmen.
The incident happened near the island of Shiashkotan, in the nothern part of the Kurile chain, nearly 1,000 km north of Japan.
Russian trawlers routinely fail to obtain licences, ignore catch quotas and tax rules and sell their illegal catch from Russian territorial waters in Japan or South Korea, a business that Russian media say is worth an estimated $1 billion a year.
Poachers usually ignore patrol boats' orders to stop and head for international waters. Border guards, who have their own patrol boats and aircraft, often fire on fleeing trawlers, but the spokesman said he could not remember a boat ever being sunk before.
On Wednesday, another Russian fishing boat took refuge in a Japanese port after coming under fire from a Russian jet when it refused border guards' order to stop and be searched.
Russian border guards have also fired on several occasions on Japanese boats said to be fishing illegally in Russian waters.
The spokesman said the chase had begun early on Wednesday when a patrol boat spotted an unidentifed Japanese-made trawler in Russian waters. "They totally ignored our stop signals and did not give a damn about our warnings," he said.
A plane summoned to the area fired warning shots and then hit the boat which caught fire but did not halt. Several hours later a U.S. reconnaissance plane detected the trawler and notified Russian border guards, the spokesman said.
A Russian jet then closed on the boat and fired at it again with its 30mm cannon. The blazing trawler communicated "injured on board" but still refused to stop, the spokesman said.
Early on Thursday, the jet launched a final attack on the boat which started to sink. Two border guard vessels were sent to the scene after the trawler stopped its engine and the crew released safety rafts, the spokesman said.
The boat sank at 0200 GMT. The border guard ship with the trawler crew aboard, was heading for the Russian far eastern port of Petropavlovsk-Kamchatsky, he said.
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