* Seeking to raise 300-350 sterling in right issue-sources
* Rejects proposed 450 pence a share cash offer
* Has consulted with major institutional shareholders
* Shares fall 2.5 percent (Adds Stagecoach no comment)
By John Bowker and Daisy Ku
LONDON, Aug 28 (Reuters) - Britain's National Express is looking to raise between 300 million pounds ($488.6 million) and 350 million in a rights issue after rejecting a proposed takeover approach led by its main shareholder.
Two sources familiar with the matter said the transport group, which operates buses in North America and Spain as well as the UK, plans to launch its rights issue after Sept. 11 when a deadline expires for the bidders to launch a final offer.
National Express said in a statement it had consulted major institutional shareholders and had decided the 450 pence a share takeover proposal -- made by 18.6 percent shareholder the Cosmen family and CVC Capital Partners -- undervalued the group.
"Strengthening of the balance sheet through an equity fundraising is the key short-term objective to unlock the inherent value of the group," National Express said, although it would not confirm the range.
National Express shares closed down 2.5 percent at 397-1/2 pence.
"We note the statement from National Express and are considering our options," a spokesman for CVC-Cosmen said, declining to comment on the prospects of tabling a higher offer.
National Express has been struggling to manage a debt pile of close to 1 billion pounds, built up via a string of acquisitions -- notably the Spanish bus operations that brought the Cosmen family onto the board.
One analyst, speaking on condition of anonymity, said he would expect the consortium to come back with a higher offer as the Cosmens look to regain control of the family business, sold to National Express in 2005.
National Express added that the proposed offer had been subject to a number of preconditions, notably the retention of two UK rail franchises that the government would like to take back under state control.
The firm said it would give up its flagship East Coast mainline franchise earlier this year after running up heavy losses.
Transport Minister Andrew Adonis said at the time that it was unacceptable for the group to continue to operate in the UK rail industry after giving up a franchise, but National Express thinks it can prove otherwise.
Bus and rail rival Stagecoach said last month it was in talks with CVC-Cosmen about potentially taking part of National Express should a bid for the company succeed.
It said earlier on Friday it was seeing slower revenue growth due to tough market conditions, and when contacted by Reuters later in the day said it had nothing to add regarding National Express. (Additional reporting by Simon Meads and Quentin Webb; Editing by Erica Billingham and Rupert Winchester) ($1=.6140 Pound)