NEW DELHI, June 17 (Reuters) - Walmart Inc’s (WMT.N) Flipkart and Amazon.com Inc(AMZN.O) have filed legal challenges against the resumption of an antitrust investigation into their business practices, according to sources and a legal filing viewed by Reuters. The Competition Commission of India (CCI) launched an investigation in January last year after a complaint accused Flipkart and Amazon of promoting select sellers on their e-commerce platforms and using deep discounts to stifle competition. The companies have denied wrongdoing and near-immediate legal challenges from the pair stalled the investigation for more than a year until a court last week ruled it could resume, having dismissed arguments that the CCI lacked evidence. The fresh appeal from Flipkart filed on June 16, argues that decision by the Karnataka court to allow the probe to resume was erroneous and must be put on hold. "Irreparable injury will be caused to the appellant if the investigation was to continue pending the present appeal," the Flipkart filing, which was not made public but has been viewed by Reuters, said. It also urged the court to quash the initial CCI order for the investigation. Amazon has mounted a similar challenge, two sources familiar with the matter said. Both are likely to be heard by a two-judge panel this week, sources said. Flipkart and CCI did not immediately respond to requests for comment. Amazon declined to comment on its appeal. Sources told Reuters this week that the CCI planned to speed up the investigation as it increases its scrutiny of big-tech firms. The CCI plans to demand information from Flipkart and Amazon on the accusations “as quickly as possible”, one source said. Such investigations usually run several months. Both Amazon and Flipkart are currently battling accusations from offline retailers that their complex business structures let them circumvent foreign investment rules for e-commerce. In February, a Reuters investigation based on Amazon documents showed it hadgiven preferential treatment for years to a small group of sellers on its Indian platform. Amazon has said it "does not give preferential treatment to any seller".