NEW YORK - The federal government will fund half of a planned $20 billion commuter rail tunnel linking New Jersey and New York under the Hudson River in an agreement announced on Thursday by the states’ governors. The broad agreement on financing is a step forward for a long-standing project that aims to alleviate congestion on one of the busiest commuter corridors in the United States. The project still is in the planning stage. National rail operator Amtrak has said it expects construction to start in 2019-2021 with completion of the tunnel in 2030. The dates are contingent on financing, Amtrak said in August. The agreement establishes the Gateway Development Corporation to oversee the project. The corporation will be run by the New York and New Jersey Port Authority, Amtrak and the U.S. Department of Transportation. U.S. Senator Charles Schumer of New York has said the project could cost at least $20 billion although Amtrak has said a reliable cost forecast has not been developed yet because the project is still in the planning and design phase. The new corporation will access low-cost federal loans to fund the states’ portion, the statement from Governors Andrew Cuomo of New York and Chris Christie of New Jersey said. Plans to build a new tunnel under the Hudson River have proved controversial because of the cost. Just after taking office in 2010, Christie canceled a Hudson River tunnel project called Access to the Region’s Core, saying the price was likely to skyrocket and citing his state’s lack of funding ability.