By Lucia Mutikani WASHINGTON (Reuters) -The number of Americans filing new claims for unemployment benefits unexpectedly fell last week as demand for labor remained strong, helping to underpin the economy amid rising interest rates and tightening financial conditions. The weekly unemployment claims report from the Labor Department on Thursday, the most timely data on the economy’s health, also showed state jobless benefits rolls declining to their lowest level since 1969 in the second-half of May. The Federal Reserve’s aggressive monetary policy stance as it fights high inflation has fanned fe…