By Donna Kardos Yesalavich Of DOW JONES NEWSWIRES NEW YORK (Dow Jones)--BP PLC's (BP) shares fell in the U.S. and London Tuesday as investors continued to worry about the extent of the oil giant's potential liabilities for the Gulf of Mexico oil spill. Its American Despositary Shares held onto most of its losses Tuesday afternoon after a federal judge in Louisiana issued an order to lift a six-month moratorium on drilling in the Gulf. The ADS were down 2.3% to $29.63 in recent trading, just above the 52-week low it hit earlier this month. In London, BP's shares closed 4.4% lower. Meanwhile, the cost of insuring BP's debt was on the rise. However, in the options market there was more volume in calls, which are considered bullish because they convey the right to buy, than in puts, which are considered bearish because they convey the right to sell. The action came as investors continued to mull over the escalating costs for BP, underscored late Monday by the Obama Administration's announcement that it sent a third bill to BP and other responsible parties, this time for $51.4 million. The amount includes expenses related to more than two dozen federal entities and agencies responding to the broken well, which is estimated to be leaking about 35,000 to 60,000 barrels of oil every day. BP already has agreed to a $20 billion escrow fund for clean-up and other expenses related to the huge oil spill flowing out of its deepwater Macondo well. It also voluntarily agreed to set aside an additional $100 million for workers who lost their jobs as a result of a deep-water drilling moratorium. The federal judge in New Orleans ruled in favor of a request by Hornbeck Offshore LLC, a small oil-services company based in Covington, La., which contends that the U.S. Department of the Interior's May 28 move to stop offshore drilling for six months after the Gulf of Mexico spill is "arbitrary" and "capricious." Its lawsuit was joined by a number of other small providers of services to the offshore oil industry. The White House said it would appeal the ruling. Ted Harper, co-manager of the Frost Dividend Value Fund and senior research analyst at Frost Investment Advisors, said the entire sector has suffered in the aftermath of the April 20 Deepwater Horizon rig explosion, and some of the negative sentiment toward BP for contributing to the share declines in the other companies could fade if the moratorium is lifted. BP had been a component in the dividend fund Harper manages, but it sold the position shortly after the oil spill started. "The rationale behind the sale was we don't know how long it's going to take to cap the spill, and we were worried about the headline and political risk, which got even more heated than I anticipated," Harper said. For now, Harper is unable to consider buying BP again because it no longer fulfills his fund's dividend qualifications. But even if he could consider it, he said would still stay away from it, at least over the near term. "I still think there's too much uncertainty around the potential liability because we haven't gotten finality on the capping of the well. It's still an ongoing effort," Harper said. "Until there's a little bit more clarity on ultimately how many barrels have spilt out, it's difficult to make an investment case for BP other than to say it may be oversold." -By Donna Kardos Yesalavich, Dow Jones Newswires; 212-416-2188; donna.yesalavich@dowjones.com (END) Dow Jones Newswires June 22, 2010 14:23 ET (18:23 GMT)