* Dollar jumps to session peak vs yen after Fed * Euro rises from four-month low against dollar * Cyprus seeking financial deal with Russia By Wanfeng Zhou NEW YORK, March 20 (Reuters) - The U.S. dollar rallied against the yen on Wednesday after a decision by the Federal Reserve to continue its aggressive monetary easing fueled optimism about the U.S. economic recovery. The euro rebounded from a four-month low against the dollar as immediate fears about a financial meltdown in Cyprus eased, with the small island country pleading for a new loan from Russia. The Fed said it will continue to buy $85 billion in mortgage and Treasury bonds per month despite growing concerns about the risks the purchases could pose. It said unemployment remains too high and fiscal policy has become somewhat "more restrictive," likely referring to the government's hefty spending cuts. The dollar initially trimmed gains versus the yen and fell further versus the euro after the Fed statement. But it quickly reversed those moves and rallied to a session high versus the yen as U.S. stocks climbed. "It's positive for risk appetite. The stock market will benefit from continued ultra-accommodative monetary policy," said Michael Woolfolk, senior currency strategist at BNY Mellon in New York. "There's been nothing in the policy statement to suggest any type of change in the Fed's stance." Gains in stocks tend to weaken the yen as investors borrow in the low-yielding Japanese unit and use the proceeds to invest in assets with greater returns. The prospect of further monetary easing in Japan added to the allure of the yen as a funding currency. The dollar rose to a high of 96.03 yen according to Reuters data, and last traded at 95.91 yen, up 0.8 percent on the day. The euro rallied 1.3 percent to 124.18 yen. The Australian dollar and sterling both gained 0.9 percent versus the yen. The U.S. central bank's meeting came as turmoil in Europe took another turn for the worse. Cyprus ordered banks to stay shut until next week as the government scrambled to come up with another plan after rejecting the terms of a bailout from the European Union. Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington, said the Fed's pledge to keep its foot on the gas pedal of monetary easing, while inherently negative for the dollar, should help the U.S. economic recovery. "The resulting upside for U.S. assets should continue to spur demand for the greenback," he said. "Moreover, the mounting uncertainty in the euro zone continues to contrast the improving backdrop in the U.S. and should add to the dollar's appeal as a safe harbor from political and economic volatility abroad." Against the dollar, the euro rose 0.5 percent to $1.2947, rebounding from $1.2843 set on Tuesday, it's lowest since late November. Analysts said the euro benefited from expectations European leaders will eventually find a solution to the Cyprus crisis, and noted there were few signs of instability in the bond markets of Spain and Italy. Some strategists said the European Central Bank's assurance on Tuesday that it was committed to providing liquidity to Cypriot banks within certain limits also helped the euro.