"If I wanted, Russian troops could be not only in Kiev, but also Riga, Vilnius, Tallinn, Warsaw and Bucharest in two days," Russian President Putin allegedly told Poroshenko, according to the German daily Sueddeutsche Zeitung.
Poroshenko is said to have relayed Putin's words to European Council President Jose Manuel Barroso during a meeting in Kiev last Friday.
Putin also allegedly warned the president of Ukraine not to rely too much on EU support, since Moscow could easily forge a "blocking minority" in the EU council to prevent decisions that Russia did not like.
Rasa Jakilaitienė, spokeswoman to Lithuania's minister of foreign affairs, told ELTA news agency that the ministry would not comment.
"We do not comment on statements made by leaders of foreign countries," she said.