Responding to talks that some EU member states would prefer to lift some of the sanctions on Russia as an encouragements and a sign of good will, Linkevičius told on the Žinių Radijas radio programme Pozicija that souch a move would be unreasonable.
"I do not think we have to encourage Russia. On the contrary, we must send a message to make Russia wake up and start behaving in the international arena," Linkevičius said on the phone from Italy.
According to him, if Russia wants to once again become an important player and contribute to solving global issues, it should " definitely not make its return to the [international] arena with the methods it uses, say, in Syria".
"This is why our messages should not be about encouraging, but about clarity and our own position. This applies not just to Syria, but to Ukraine as well.
"No one is very proud of the language of sanctions or believes that it's the way to communicate with nations, but when it is the only way to make ourselves heard and understood we need to continue with it.
"We've recently spoken about it not just here, in Italy, but I talked with foreign policy advisers of the German chancellor in Berlin. I sensed the same inclination to continue the policy."
Linkevičius has noted that there have always been sceptics regarding the Russia sanctions among the EU members, saying that trade is better than war.
"Certainly, no one is going to wage war and we do not intend to raise tensions from our side," Linkevičius responds, "but we must not disregard our principles, values, commitments."
Any leniency on the EU's part, according to Linkevičius, will be interpreted as a go-ahead for Moscow to continue pursuing its hostile policies.
After a Malaysia Airlines passenger plane was shot down over the rebel-controlled territory in eastern Ukraine, the EU imposed sanctions on Russia's financial, military industry and energy sectors in July last year.
In March 2014, the EU Council had also instituted asset freezes and travel bans for Russian officials connected to the aggression against Ukraine. The sanctions were extended for six more months earlier this year.
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