The Food and Drug Administration rejected Merck & Company's request to market a successor to its withdrawn arthritis drug Vioxx in the United States, the drug maker said. The decision was widely expected, after a panel of F.D.A. advisers two weeks ago voted 20-1 against approving the drug, Arcoxia. Arcoxia is in the class of anti-inflammatory drugs called Cox-2 inhibitors, which are touted as less likely to cause stomach bleeding or have other dangers, but they have been linked to heart risks. It is the same class of drugs as Vioxx, which has become a poster child for drug safety problems. Merck pulled Vioxx from the market in 2004 after research showed that it doubled risk of heart attacks and strokes. A Merck spokesman said the company would not discuss whether it now will drop efforts to get Arcoxia approved domestically.