(Adds auction results, quote, updates prices) * Trump says not ready to make deal with China * EU may impose fine on Italy -Salvini * Treasury sells two-year notes to strong demand By Karen Brettell NEW YORK, May 28 (Reuters) - Concerns about the U.S.-China trade war and Italy's budget policy sent benchmark U.S. Treasury yields to their lowest levels since September 2017 on Tuesday and helped fuel demand for Treasury Department debt auctions. U.S. President Donald Trump said on Monday that Washington was not ready to make a deal with China, but he expected one in the future. At the same time, he pressed Japanese Prime Minister Shinzo Abe to reduce Japan's trade imbalance with the United States. The European Commission, meanwhile, could impose a 3 billion euro ($3.36 billion) fine on Italy for breaking EU rules due to its rising debt and structural deficit levels, the country's Deputy Prime Minister Matteo Salvini said on Tuesday. Salvini, whose far-right League party triumphed in European elections on Sunday, said he would use "all my energies" to fight what he said were outdated and unfair European fiscal rules. "It's very much the usual suspects in terms of the drivers behind the risk off sentiment," said Ian Lyngen, head of U.S. rates strategy at BMO Capital Markets in New York. The safe haven bid for U.S. debt helped the Treasury sell $81 billion in two-year and five-year notes to strong demand, even with two-year yields near their lowest levels since February 2018 and five-year yields at the lowest since December 2017. A $40 billion sale of two-year notes had the strongest demand in nine months, with a bid-to-cover ratio of 2.75. "The two-year auction is a reflection of the overall strength of the market even as yields have hit new cycle lows," said John Canavan, an analyst at Oxford Economics in New York. A $41 billion sale of five-year notes was solid, if not as strong as the two-year note auction. The notes had a bid-to-cover ratio of 2.38, below the 2.44 level reached at the prior five-year note auction held in April. The Treasury will also sell $32 billion in seven-year notes on Wednesday. Concerns about global growth, in part due to international trade tensions, and tepid inflation has increased expectations that the U.S. Federal Reserve will cut rates this year. Interest rate futures traders are pricing in an 80% chance of a rate cut by December, according to the CME Group's FedWatch tool. (Additional reporting by Richard Leong; Editing by Richard Chang) )