NEW ORLEANS, April 23 (Reuters) - A federal appeals court has agreed to speed up the process of determining whether BP Plc's settlement with class-action plaintiffs over the 2010 Gulf of Mexico oil spill is being handled properly. BP had asked for the case to be heard as early as late May, and the Fifth Circuit Court of Appeals in New Orleans agreed late on Monday to an expedited appeal, but denied BP's request that payments be suspended until the appeal outcome is known. U.S. District Judge Carl Barbier in early April told BP he saw no reason to interfere with the current payout process, despite BP's complaint that frivolous and even "fictitious" claims are being paid. The source of dispute is the calculation of business economic losses, for which just shy of $800 million has been paid out on 4,870 claims so far, according to the program's official website. As of Tuesday, more than 168,000 claims have been submitted under the entire Deepwater Horizon Economic and Property Damages Settlement, according to the website, and a total of $1.96 billion of payments had been made on 29,413 claims. BP, in a March court filing, listed two dozen examples of "unjustified windfall payments" calculated through formulas stipulated in its settlement with thousands of class-action plaintiffs, including individuals and businesses who say they were harmed economically by the worst U.S. offshore oil spill. BP complained that the court-appointed claims administrator, Patrick Juneau, was misinterpreting the formulas to the benefit of plaintiffs. BP initially estimated it would pay a total of $7.8 billion through the settlement, but it was not capped, and the company later put it at $8.5 billion before reducing it back to $7.7 billion to underline its disapproval. Last week saw the end of the first phase of the trial under Barbier over all the claims brought by the U.S. government, Gulf Coast states, and private parties affected by the spill. Legal briefs will now be filed for a few months, before the September start of the next phase to determine how much oil spilled. That case is In re: Oil Spill by the Oil Rig "Deepwater Horizon" in the Gulf of Mexico, on April 20, 2010, U.S. District Court, Eastern District of Louisiana, No. 10-md-02179. The appeal is "BP Exploration & Production Inc et al. vs Lake Eugenie Land & Development Inc, et al." in the U.S. Court of Appeals for the Fifth Circuit, No. 13-30329.