Priceline launched a fare sale Tuesday, promising to shave an additional 10 percent off its already discounted fares, said a company spokesman. The sale comes a week after Hotwire, Priceline's chief competitor in the discount travel sector concluded its fare sale. Competition among discount travel agencies has begun to heat up as prices for airline tickets decline. The lull in the travel sector has prompted airlines to cut prices, and that means travel sites that offer retail fares can sometimes offer tickets for the same price or lower than discount travel sites. Brian Ek, a Priceline spokesman, said the fare sale, which offers a reduction of as much as 50 percent off some ticket prices, will last through June 5 and travel must take place before July 1.