By Gabriela Baczynska

BRUSSELS (Reuters) - A European Parliament committee on Monday backed visa-free travel to the European Union for Georgia and moved toward granting another ex-Soviet republic, Ukraine, the same right, after migration worries delayed the process before the summer.

The committee voted 44 in favor versus five against for the Georgian liberalization, although the decision must still be approved in the so-called 'trilogue' negotiations between the parliament, EU states and the executive European Commission.

EU states held off an expected decision to ease travel rules for Georgia in June as Germany and other countries voiced reservations, saying any new visa waivers should be delayed until the bloc agreed easier rules to suspend visa-free travel.

That process is now also awaiting trilogue talks.

Ahead of an expected vote by the committee later this month, Mariya Gabriel, a Bulgarian lawmaker with the parliament's largest faction, the European People's Party, told Monday's session that travel rules should also be relaxed for Ukraine.

"Politically and strategically it is very important that we deliver visa-liberalization for Ukraine," said another member of European Parliament, Portugal's Ana Gomes of the Socialists.

Like Georgia, Ukraine sees visa-free travel to the EU as part of a geopolitical tussle with Russia over the ex-Soviet states' Western aspirations, which Moscow opposes.

The issue of fostering closer ties with the EU was at the heart of mass street protests in Kiev that toppled a Moscow-allied president there in early 2014.

Moscow responded by annexing Crimea from Kiev that March and unrest then spread to eastern Ukraine, where Russia-backed militias took up arms against Kiev government troops in a conflict that killed more than 9,500 and remains unresolved.

The EU, as well as the United States, slapped sanctions on Russia over the turmoil in Ukraine. While a growing number of EU states now speak of the need to re-engage with Russia, the lawmakers on Monday stressed the EU stood by Ukraine.

Georgia was at the heart of international tensions in 2008 when a five-day war between Tbilisi and Moscow in August led to the previous sharp decline in ties between Russia and the West.

The south Caucasus country of 3 million is due to hold parliamentary elections in October.

In a sign that the European Parliament wanted another hopeful, Kosovo, to do more before it is given visa-free travel, the lawmakers endorsed a corresponding proposal, but did not give their negotiators mandate to open the trilogue talks.

The EU says Kosovo must ratify a border deal with Montenegro before it can get more relaxed travel rules to the bloc. But the frontier deal is controversial in Kosovo and final parliamentary approval has been delayed.

The EU is also in uneasy talks on granting visa-free travel to Turkey, though both Ankara and Brussels now admit that will be delayed from a previous target date of October.

(Editing by Catherine Evans)