* Euro trades near four-month lows vs dollar * Cypriot banks open amidst tight capital control measures * Italy's funding costs rise as political worries persist * Yen slide loses downward momentum as BOJ meeting awaited By Anooja Debnath LONDON, March 28 (Reuters) - The euro traded near four-month lows against the dollar on Thursday, remaining vulnerable to the crisis in Cyprus where banks reopened after the imposition of capital controls. The euro has been undermined this week by concerns that Cyprus's $10 billion euro rescue deal, which will leave big depositors and private bondholders with huge losses, could become a template for future bank bailouts in the euro zone. That could encourage anxious investors to sell euro zone assets and prefer the safety of the dollar, the yen, the Swiss franc or even the British pound. Those concerns along with continued political uncertainty in Italy, and a weak economic outlook across the euro zone would keep the euro pinned down, analysts said. Rising bond yields in Slovenia, a possible next pain point for the euro zone, also hurt the currency. The euro was up 0.2 percent on the day at $1.2800, within site of a four-month low of $1.2750 hit on Wednesday. Traders said month-end demand from investors rebalancing their bonds and stocks portfolio would offer it some support, but any bounce towards Wednesday's high of $1.2867 could see fresh selling. "Investors have been focusing on the events in Cyprus and political uncertainty in Italy and this has weighed on the euro," said Michael Sneyd, FX strategist at BNP Paribas. However, he said that the markets have perhaps been a bit too aggressive on betting against the euro, so it remained vulnerable to a short squeeze higher in the near term on any positive news out of the bloc. Banks in Cyprus opened for the first time in nearly two weeks on Thursday under tight controls to prevent a run on deposits. Although these measures prevented a rush of flows out of the island's banks, some analysts said curbing the free flow of cash in Cyprus was bad for the bloc. "Economic and monetary union across the entire euro zone no longer exists. Even though the country (Cyprus) is very small, policymakers' willingness to suspend cross-border euro convertibility is a meaningfully negative signal for the euro zone," George Saravelos, FX strategist at Deutsche Bank, said in a note. Apart from worries in Cyprus, political confusion in Italy saw its borrowing costs rise on Wednesday and hurt the euro. Italian centre-left leader Pier Luigi Bersani faced only a slim hope of forming a government after talks with rival party leaders ended with rejection from Beppe Grillo's 5-Star Movement. YEN STEADY Given the problems in the euro zone, investors chose the safety of the more liquid yen. The euro was up 0.1 percent against the Japanese currency at 120.80 yen, recovering slightly from a one-month low of 119.745 hit earlier in the day. The yen also gained on talk of repatriation flows by Japanese investors before the end of the financial year on March 31. That gave the currency a reprieve after a period of sustained weakening due to expectations - now heavily priced in - of aggressive monetary easing by the Bank of Japan at new governor Haruhiko Kuroda's first policy review on April 3-4. Some analysts see the risk for disappointment, given high expectations of aggressive easing from the Bank of Japan. That could give the yen a boost towards the 95 yen level after the BOJ meeting. The dollar was down 0.2 percent at 94.27 yen with bids to buy the U.S. currency cited at 94 yen. U.S. data including jobless claims, the final reading of fourth-quarter gross domestic product and the Chicago PMI are all due on Thursday and better-than-expected numbers could give the dollar a boost.