The border guards saw the Pyotr Kotsov vessel leaving a Tallinn port and making strange maneuvers in the Estonian waters.
"In response to a question from Estonian border guards, the Russian sailors said they were conducting research. Since they did not have proper permission, the border guards asked them to [turn their] course towards the Naissaar Island for verification of documents," the Border Guard service said in a statement.
The border guards said the vessel headed for the island, but then changed its course and headed north-west intending to leave Estonian waters.
The border guards decided not to use force to stop the Russian vessel, but Estonian coast guard vessels, the Vapper and the Kati, escorted the Pyotr Kotsov out of Estonian waters.
"The crew of the Russian research vessel violated the law on Estonian territorial waters [and] the UN Sea Convention of 1982 and failed to follow orders from Estonian border guards," the Border Guard service said. "All violations made by the Russian vessel were documented. An investigation has been launched. The proper Russian bodies have been informed about the incident."