KYIV, Jan 5 (Reuters) - The European Union"s top diplomat visited the frontline of Ukraine"s war with Moscow-backed forces on Wednesday, promising "massive consequences and severe costs" for Russia if it launched a new military offensive against its neighbour. Josep Borrell flew by helicopter to the easterly Luhansk region, the first EU High Representative to do so since the outbreak of the conflict in 2014, as part of a Western diplomatic push in support of Ukraine. Kyiv and its allies have sounded the alarm over the build-up of tens of thousands of Russian troops and military equipment near Ukraine"s borders in recent weeks, raising fears of an open war between the two ex-Soviet neighbours. TV footage showed Borrell walking through a snowy landscape, meeting soldiers and civilians at one of the checkpoints that divides government-controlled Ukraine from the separatist-held territories. The roofs of nearby houses were destroyed and had bullet holes in the walls. "The conflict on the borders is on the verge of getting deeper and tensions have been building up with respect to the European security as a whole," Borrell told reporters. The EU has a firm stance and a strong commitment "that any military aggression against Ukraine will have massive consequences and severe costs", he added. The Kremlin did not immediately issue a public response to Borrell"s visit. Moscow has previously denied planning a new military offensive against Ukraine and accuses Kyiv of building up its own forces in the east of the country. Russia has pressed the United States for security guarantees that NATO will halt its eastward expansion. The two sides will meet for talks in Geneva on January 9-10. Ukraine has long sought assurances that no decisions about its future, including its right to eventually join the EU and the NATO military alliance, would be made without its involvement. Borrell too insisted that the security of Ukraine affected the security of Europe as a whole, and that the EU had to be involved in discussions with Russia. "There is no security in Europe without the security of Ukraine. And it is clear that any discussion on European security must include the European Union and Ukraine," Borrell said. Ukrainian Foreign Minister Dmytro Kuleba, who accompanied Borrell, welcomed the trip as "a very timely visit against the background of Russian blackmail, escalation and threats." Relations between Kyiv and Moscow collapsed after Russia annexed Crimea in 2014 and Moscow-backed forces seized territory in eastern Ukraine that Kyiv wants back.