BRUSSELS (Reuters) - Ukrainians' hopes of securing visa-free travel to the European Union received a boost on Monday when a key committee of the European Parliament backed their cause, but further hurdles remain.

Ukraine, an ex-Soviet republic of 45 million people, faces stiffer resistance from some EU member states at a time of heightened public concern over immigration after more than a million migrants and refugees arrived in the bloc last year.

The European Parliament's Civil Liberties, Justice and Home Affairs committee backed the proposal for visa-free travel for Ukraine by 38 votes to four against.

A team of lawmakers will now start negotiations on the matter with the European Council, which brings together representatives of the EU member states.

The powerful duo of Germany and France oppose granting more visa-free movement before the bloc has beefed up an emergency mechanism that will allow the swift suspension of more lenient travel rules in the event of a sharp increase in immigration.

Negotiations on this so-called 'suspension mechanism' have ground to a halt, denting the hopes for visa-free travel to the EU of another former Soviet republic, Georgia.

Ukraine is also a more complicated case for the EU as it is much bigger than Georgia and shares a direct border with EU countries such as Poland, Slovakia and Hungary, which are part of Europe's Schengen zone of free travel.

The EU backs Ukraine in its confrontation with Russia, which annexed the Black Sea peninsula of Crimea from Kiev in March 2014 and sides with rebels who later took up arms against government troops in Ukraine's industrial east.

But some EU states are frustrated with what they see as Kiev's slow progress on social and economic reforms, including fighting rampant corruption.

(Reporting by Gabriela Baczynska; Editing by Gareth Jones)