"We are talking about a practical level on which much can be done. As to any changes to our political stance, there are no reasons for that," Linkevičius told the reporters after the meeting.
In the minister's words, the politicians and diplomats did not discuss an improvement in Lithuania's relations with Russia.
"That issue was not discussed today. I'm saying once again: there are no goals or reasons for changing the political stance," he said.
According to Linkevičius, a warming of ties with Russia can only happen at Moscow's initiative.
"Any warming must come from their side, from those who cool (relations). I categorically reject suggestions that we should do something to improve ties," the minister said.
"I've already told you, perhaps, more than on one occasion: we didn't occupy Crimea, we didn't occupy 20 percent of Georgia's territory, we didn't interfere in the political system or elections of other countries, and we don't see anything for us to improve here," he said.
"If someone imagines an improvement in relations through concessions in these areas, then this won't happen".
Skvernelis told reporters ahead of Monday's meeting that it was important to keep to the fundamental principles in relations with Russia.
The prime minister also said that Grybauskaitė and he did not differ in their positions on ties with Russia.
"As regards international relations, the fundamental principles can't be violated: human rights and international commitments are paramount. I'm very clear and strict on that," Skvernelis said.
"As to the sanctions that are in place, they must be effective. There's no divergence in any positions here. The president and I share the same position. I see no divergence at the strategic level," he added.
Skvernelis early this year called for resuming political contacts with Russia, triggering criticism from Grybauskaite.
Remigijus Motuzas, Lithuania's ambassador to Moscow, told BNS that a Lithuania-Russia bilateral intergovernmental commission had held its last meeting back in 2012, adding that there was no discussion at Monday's meeting about resuming its activities.
He noted, however, that there was active cooperation at a lower level.