Jan 12 (Reuters) - Warner Bros Discovery Inc is raising HBO Max's ad-free subscription fee in the United States for the first time since the streaming service was launched in 2020, the TV network said on Thursday, sending its shares down 3%.Prices for the platform, currently streaming shows such as "The White Lotus" and "House of the Dragon", will rise by $1 to $15.99 plus taxes a month for U.S. subscribers.HBO Max, which also has an ad-supported tier, faces pressure from slowing user growth and tight competition from larger rivals Netflix Inc and Walt Disney Co's Disney+. Netflix and Disney had also raised prices for some of their streaming services last year.Warner Bros Discovery, formed last year by the merger of AT&T Inc's WarnerMedia unit and Discovery Inc, is pushing for internal changes including plans to combine HBO Max and Discovery+.The media company last month said it expected costs related to content write-offs to rise by $1 billion to as much as $3.5 billion.It also made both HBO Max and Discovery+ available on Amazon.com Inc's Prime Video platform in select markets. (Reporting by Yuvraj Malik in Bengaluru; Editing by Devika Syamnath)