Brussels says that about 2,700 migrants -- most from Iraq -- have crossed illegally into the Baltic state and EU member in recent months.

Officials suspect the influx is being orchestrated by the Belarusian regime in retaliation against EU sanctions, with flights ferrying migrants from Baghdad to Minsk.

"We have been in contact with the Iraqi government in order to better control flights to Belarus and re-admit Iraqi nationals who want to return voluntarily or have no right to international protection," Home Affairs Commissioner Ylva Johansson wrote in a letter to EU ministers.

EU foreign policy chief Josep Borrell said on Wednesday that he had held talks with Iraq's foreign minister "on how to tackle increased number of Iraqi citizens irregularly crossing from Belarus into Lithuania".

"This is an issue of concern not only for one member state but for the entire EU. We count on Iraq's support," Borrell wrote on Twitter.

Baghdad pledged earlier this month to investigate the alledged smuggling of people to Lithuania and has set up a joint committee with the EU to discuss migration matters.

A spokesman for the bloc said on Thursday that "a large part" of those crossing into Lithuania did not appear eligible to claim asylum in the EU.

Brussels has threatened to ratchet up sanctions that it has slapped on Belarus since last year over a crackdown on protests against a disputed elections.

The EU last month hit key sectors of the Belarusian economy after Minsk forced a European airliner to land in order to arrest a dissident journalist.