The dollar remained near 13-month highs on Tuesday ahead of U.S. inflation data, with investors focused on price pressures amid rising oil prices and Federal Reserve Chair Kevin Warsh's first semiannual testimony to Congress. U.S. and Iranian forces traded attacks in the Gulf, pushing oil toward $90 a barrel and raising the perceived chance of global interest rate increases this year. Markets show a 20% probability of a Fed rate hike in July, which has lifted U.S. Treasury yields above 4.6% and supported the dollar. The euro rose 0.2% to $1.1399, sterling gained 0.2% to $1.337, and the yen edged 0.1% higher to 162.27 per dollar but remained near 40-year lows, keeping traders alert for possible official buying from Tokyo.