Aug 9 (Reuters) - Australia"s consumer regulator filed separate lawsuits against the country"s top three internet service providers for allegedly making incorrect claims about speeds that the companies say are partly the fault of the government-backed broadband provider. Telstra Corp (TLS.AX), Optus and TPG Telecom (TPG.AX) are alleged to have made incorrect claims about the maximum speed of the internet connections they offer and also accepted payments from some customers for plans without providing the promised speeds, the Australian Competition and Consumer Commission (ACCC) said in a notice on Monday. In Australia, the state-owned National Broadband Network (NBN) acts as the wholesale provider of broadband which the internet service providers then offer to their customers. TPG said it would offer affected customers a refund, while Telstra and Optus said they would offer remedial options to customers. TPG said the issue was due to the "failure by NBN Co to provide timely and accurate speed information to TPG Internet," and its own legacy processes from 2017 that have been fixed. "The customer doesn"t receive what they want, the RSP (Retail Service Provider) still pays full price, and NBN Co have limited obligations to do anything about it and continue to charge RSPs for a plan they know the connection may not deliver," said Michael Ackland, Telstra"s head of consumer and small business. The regulator said Telstra and TPG made incorrect statements to customers between April 2019 and April 2020, while Optus made them through 2019. "Collectively, hundreds of thousands of consumers were allegedly misled by these three big internet providers," ACCC chair Rod Sims said. "What makes this behaviour even more concerning is that Telstra, Optus and TPG were well aware of these issues and had earlier given undertakings to the ACCC to provide remedies to consumers." The ACCC is seeking penalties, without specifying an amount, among other orders.