Russian hackers took down public and private websites in Lithuania on Monday in retaliation for Vilnius' decision to stop the transit of some goods under European Union sanctions to a Russian exclave.

Lithuania's tax authority said in a statement it had halted all activities due to an unusually large number of attempts to connect to its systems, although all data was safe.

"The main targets are state institutions, transport institutions, media websites," Deputy Defense Minister Margiris Abukevicius said, in another sign of deteriorating relations between the Baltic NATO country and neighboring Russia because of Moscow's invasion of Ukraine in February.

Russian hacker group Killnet claimed responsibility for what is known as a distributed denial of service (DDoS).

"The attack will continue until Lithuania lifts the blockade," a Killnet spokesperson said. "We have demolished 1,652 web resources. And that's just so far."

The Russian exclave of Kaliningrad is sandwiched between EU and NATO members Poland and Lithuania and supplied by rail via Lithuanian territory.

Lithuania had begun to see signs of an attack as early as June 21, Abukevicius said.

A Russian Security Council spokesperson on June 22 promised retaliation over the blocked shipments, stating that these would have "a serious negative impact on the population of Lithuania."

"It is very likely that attacks of similar or greater intensity will continue in the coming days, especially in the transportation, energy and financial sectors," Lithuania's National Cyber Security Centre said in a statement.

The secure network used by state institutions was also among those affected, the center said.

European Union foreign policy chief Josep Borrell said last week that Lithuania "only applies the European Union sanctions" in ceasing transport of certain goods to Kaliningrad, and has not taken any unilateral decisions.