WASHINGTON - New US claims for unemployment benefits were unchanged last week, holding at the lowest level since the early days of the 2007-2009 recession and giving a fresh sign the battered labor market is healing.Workers filed 351,000 initial claims for state unemployment benefits, the Labor Department said on Thursday."It's broadly in line with recent US data showing a gradually improving economic backdrop," said Omer Esiner, a market analyst at Commonwealth Foreign Exchange in Washington.The last two weekly readings have been the lowest since March 2008.