BRUSSELS (Reuters) - European Commission head Jean-Claude Juncker has invited the leaders of four eastern European countries to a dinner, according to a letter seen by Reuters, in an effort to ease tensions between them and wealthier western member states. In his letter, dated Oct. 2 and addressed to the leaders of Poland, Hungary, the Czech Republic and Slovakia, Juncker stressed the  paramount importance  of EU unity, strained by disputes over immigration and other issues as well as by Brexit. While Prague and Bratislava have sometimes struck a more moderate tone, Warsaw and Budapest have constantly been at loggerheads with the bloc s executive Commission in Brussels, as well as with EU heavyweights Germany and France, over what the bloc increasingly sees as their flouting of democratic rules. Juncker proposed a dinner with the leaders of the four  Visegrad group  nations in Brussels on Oct. 18, ahead of an EU summit on Oct. 19-20, citing the need to build  a more united, stronger and more democratic Europe  despite Britain s exit.  I believe that preserving the unity of the (remaining) 27 in this process is of paramount importance,  he said. The eastern states, especially Poland and Hungary, have resisted an EU program for all member states to accept refugees after a mass influx of people in 2015-16, mostly Muslims from the Middle East and Africa. Other points of contention include a reform of EU s labor rules, which France and some other western states say give unfair competitive advantage to cheap workers from the east. Some western countries, notably Italy - on the frontline of taking in refugees and migrants from across the Mediterranean - have suggested cutting the generous aid provided to the easterners through the EU budget if they fail to show European  solidarity  over migration. Slovak Prime Minister Robert Fico s recent reassurances that his country, a member of the single-currency euro zone, sees itself firmly at the heart of the EU seem to have gone down well in Brussels. The Commission has responded by saying it would work with Slovakia and other eastern member states in tackling what they see as the malpractice of second-class food products being sold by big Western multinationals on their home markets. Soothing relations with Poland and Hungary, however, will prove more challenging.  Poland, led by the eurosceptic Law and Justice party (PiS), is under an unprecedented EU investigation over the rule of law following a series of reforms that critics say threaten the independence of the Polish judiciary. The EU also faces a tough challenge agreeing its next multi-year budget that runs from 2021, with generous handouts to the eastern nations under particular threat as Britain, a leading net donor,  prepares to leave the bloc in 2019.      After pro-EU centrist Emmanuel Macron won the French presidency this year, Brussels hopes a reinvigorated Paris-Berlin alliance can help usher in reforms needed for the bloc to thrive despite Brexit.  The Franco-German axis is promising to be the strongest in years. They (the easterners) either play along that   or they lose,  a senior EU diplomat said. 