The president said that the Zapad 2017 exercise was one of the main pieces of evidence of the Kremlin's inability.
"The Zapad exercise is just one symptom of the Kremlin's inability to finally end its hatred towards the West," she told the UN General Assembly.
In her words, with the drills, the Kremlin is "training its army to attack the West." Lithuania and other countries in Central and Eastern Europe have repeatedly expressed concerns over the Zapad scenario and scope.
Although the UN General Assembly is focused on North Korea, Iran and the situation of Rohingya Muslims in Myanmar, Grybauskaite urged global leaders to turn back to Eastern Europe where Russia applies "the same methods of blackmail, bullying and aggression."
"Despite Russia's special responsibility to protect international peace as permanent member of the Security Council, it violated the UN Charter by attacking Georgia, illegally annexing Crimea, and directly participating in the war in Eastern Ukraine," said the Lithuanian president.
Reforms of the organization, which was established after World War II, was also high on the agenda of the New York meeting of UN leaders.
US President Donald Trump and UN Secretary General Antonio Guterres mainly talked about the need to reduce the degree of bureaucracy, thus enhancing the organization's capacity.
Lithuania joined the Trump-initiated political declaration, which is aimed at reforming the United Nations, while Grybauskaite stated the organization had failed to defend the world against wars and instability.
"Now we face the choice: either we give this organization the voice to rise against the abuse or we will make it irrelevant," said the Lithuanian president.
The UN includes 193 states.
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