WASHINGTON, April 13 (Reuters) - U.S. consumer prices increased by the most in more than 8-1/2 years in March and underlying inflation picked up as more parts of the economy reopened thanks to increased vaccinations and massive fiscal stimulus. The consumer price index jumped 0.6% last month, the largest gain August 2012, after rising 0.4% in February, the Labor Department said on Tuesday. Excluding the volatile food and energy components, the CPI rose 0.3%. The so-called core CPI nudged up 0.1% in February. Economists polled by Reuters had forecast the overall CPI advancing 0.5% and the core CPI climbing 0.2%. (Reporting by Lucia Mutikani, editing by Ed Osmond)