By Ayesha Rascoe and Valerie Volcovici WASHINGTON, June 13 (Reuters) - Delays in approval of more natural gas export projects are costing U.S. companies millions of dollars a day and giving a leg up to rival countries also looking to boost exports, the chief of Exxon Mobil Corp said on Thursday. The comments by Exxon's Rex Tillerson came hours after new U.S. Energy Secretary Ernest Moniz told lawmakers he hopes to "expeditiously" begin evaluating the more than a dozen applications awaiting approval to export liquefied natural gas (LNG). "It's a very competitive marketplace. It's not like people are just going to stand at our door like panting dogs just waiting for us to give this (LNG) to them," Tillerson said while answering questions after an event at the Asia Society focused on Asian energy security. Tillerson said he left a meeting with Moniz on Wednesday with no clear idea of when the company's Golden Pass LNG project - a $10 billion joint venture with Qatar Petroleum - would be approved. "I don't want to start on this process if you tell me its going to take five years for you to get around to my application," Tillerson said. U.S. companies need authorization from the Department of Energy to export gas to all but a handful of countries with free trade agreements. Japan and India are among the countries keen to gain access to U.S. supplies. The Energy Department ended a two-year freeze in reviewing liquefied natural gas (LNG) export applications in May, when it approved gas exports to all countries from Freeport LNG's terminal in Texas. Shortly after that move Moniz, who was sworn in on May 21, said he would undertake a thorough review of the gas export review process, promising to ensure that current data was being used to make these decisions. At his first appearance at a Congressional panel since his swearing-in, Moniz told lawmakers at a House Energy and Commerce committee hearing on Thursday the review should wrap up soon. "We're getting ready to begin evaluating the dockets on a case-by-case basis," Moniz said. There would "absolutely" be additional decisions this year, he added, without giving a more specific time frame. Companies have lined up to export excess gas produced from the nation's shale boom. The gas can fetch higher prices abroad. Other backers of proposed export projects include Dominion Resources Inc, Sempra Energy, BG Group Plc and Veresen Inc. Some lawmakers and a group of manufacturers led by Dow Chemical Co, have called on the department to be cautious, arguing that unfettered exports could harm the U.S. economy by raising the price of gas at home.