The trawler Electron, accompanied by the Russian anti-submarine frigate Admiral Levchenko which joined it at midnight, "crossed into Russian territorial waters at 0328 Moscow time (2328 GMT Tuesday) and are going to Murmansk along the border," the Russian navy spokesman Igor Dygalo said as quoted by the ITAR-TASS news agency.
"On the other side of the border, they are trailed by the Norwegian ships in constant communication with the Admiral Levchenko," Dygalo said, adding assurances that "the situation is under control and is not conflictual."
The Electron took off with two Norwegian inspectors, who had stopped the vessel to investigate it for illegal fishing in the Barents Sea, on Saturday, and had been fleeing the Norwegian coast guard since then.
Norway claims full sovereignty of the waters in the Svalbard archipelago in the Arctic, where the Electron was stopped, but Russia does not recognize that claim.
After the two inspectors boarded the Elektron it initially headed for Tromsoe in northern Norway on orders from the Norwegian authorities, but then changed its route on Sunday and has since refused to comply with Norwegian demands.
Russian and Norwegian officials said they expected a diplomatic solution to be found.
Norwegian and Russian authorities have been in contact several times over the issue and Oslo has stressed that there is no diplomatic tension between the two neighbours.
However, Russian industry observers said the incident could affect a bilateral fisheries commission meeting set to be held next week between Norway and Russia.