* Growing optimism that Greece can renegotiate bailout terms * Fed expected to opt for more stimulus * Australian dollar rises to 6-week high vs dollar By Wanfeng Zhou NEW YORK, June 19 (Reuters) - The euro rallied against the U.S. dollar and Japanese yen on Tuesday, buoyed by positive news out of Greece and as a run-up in Wall Street stocks encouraged investors to take on riskier positions. Traders scrambled to cover bets against the euro as fears of Greece exiting the euro zone receded following a weekend victory for pro-bailout parties. Greek parties holding talks to form a government are likely to strike a deal by Wednesday, said Socialist leader Evangelos Venizelos. Adding to the positive sentiment, international lenders and Greece will renegotiate the program on which the second financial bailout for Athens is based because the original has become outdated, a senior euro zone official said. Strategists said the euro would struggle to rally beyond the one-month high of $1.2748 posted on Monday, given worries about Spain's banking system and the euro zone's dire economic outlook. "Essentially, this is an adjustment process from a severely short risk position that was in place going into last weekend," said Michael Woolfolk, senior currency strategist at BNY Mellon in New York. The euro rose 0.9 percent to $1.2683 after hitting a session high of $1.2730 on Reuters data, partly helped by demand in the Middle East. Support is seen around $1.2536, the trendline drawn below daily lows from June 1, and the 21-day moving average around $1.2530. It trimmed gains after a German government official said there was no discussion at a Group of 20 leaders summit in Mexico this week about using Europe's rescue funds to buy up the bonds of stricken members of the euro zone. British media reports earlier said German Chancellor Angela Merkel was poised to use Europe's dual bailout funds, known as the EFSF and ESM, to buy up the debt of countries like Italy and Spain, and had discussed such plans at the summit. News that a second, more detailed audit of Spanish banks would be delayed until September fuelled more bearishness toward Spain, the euro zone's fourth-largest economy, whose 10-year borrowing costs have ballooned above 7 percent. Spain's Treasury sold 12- and 18-month debt on Tuesday at yields of over 5 percent, compared with just under 3 percent at the last auction for the same maturities in May. It is to sell between 1 billion and 2 billion euros of bonds on Thursday. "We believe sustained high yields will eventually force Spain into taking a full-fledged bailout," wrote Brown Brothers Harriman in a note, adding that the delay in the results of Spain's banking sector audit would not sit well with investors. "The market simply does not have this kind of patience." Against the yen, the euro was up 0.6 percent at 100.14 . The dollar slipped 0.2 percent to 78.93 yen. FED DECISION Hopes that the Federal Reserve's policymakers will agree on extending stimulus measures fueled a rally in stocks and undermined the safe-haven appeal of the U.S. dollar. The Fed will announce its policy decision Wednesday afternoon and speculation is rising it could opt for a third round of so-called quantitative easing as Europe's troubles pose a risk to growth in the United States. Many analysts expect the Fed to extend its long-term bond-buying through "Operation Twist" by a few months from the current deadline of June. "There is positioning ahead of the Fed, with the dollar unable to capitalize on euro-negative sentiment ahead of the Fed," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington. "The risk is relatively high that officials will signal the need for more stimulus." Another round of easing would weigh on the U.S. dollar and boost growth-linked currencies like the Australian dollar. The Australian dollar jumped to a six-week high of 1.0202. It was last trading up 0.6 percent at $1.0185. The dollar index, which measures the greenback against a basket of major currencies, was down 0.7 percent at 81.388, having struck a one-month low of 81.266 on Monday.