* All trading systems at NSE operating normally
* NSE suffered a major tech disruption on Monday
* Brokers seek reassurance from NSE, eye rival BSE
* NSE chairman calls glitch 'black swan' event - letter (Updates with letter from NSE chairman to employees, NSE statement)
By Rafael Nam and Abhirup Roy
MUMBAI, July 11 (Reuters) - India's National Stock Exchange operated normally on Tuesday, a day after a technical glitch caused a five-hour disruption in trading, but rattled traders demanded that the country's biggest exchange quickly take measures to prevent a recurrence.
All trading systems at the NSE, including price quotations for individual stocks, were operating, with share volumes recovering and the broader NSE index rising as much as 0.6 percent to a second consecutive record high.
But brokers said the disruption, the biggest to hit the country's exchanges, had dented confidence in the NSE at a time when its plans for an initial public offering (IPO) had already been halted by a regulatory investigation into whether it provided unfair access to its servers to some brokers.
In a letter to employees on Tuesday, NSE Chairman Ashok Chawla acknowledged the exchange had suffered a number of challenges this year, and called the technical glitch on Monday "one more straw on the camel's back".
However, he defended the company's response as appropriate, without providing further details on what caused the disruption.
Chawla described Monday's problem as a "black swan" event, or something very unusual and difficult to predict.
"It unfortunately puts the NSE in the spotlight for the wrong reasons. We have handled this effectively, which is indeed our responsibility as the largest exchange of the country," Chawla wrote in the letter, a copy of which was seen by Reuters.
The NSE said in a statement trading had been normal on Tuesday and it would "continue to work to improve the systems to avoid any recurrence of such eventualities in the future".
The NSE, which is expected to release a detailed report explaining the reason for the disruption, faces criticism for the length of time it took to resolve it, and the conflicting messages to brokers as the exchange tried several times to restart trade.
Some traders said they were looking to open trading accounts with rival BSE Ltd, even though its trading volumes are only a fraction of the NSE's. A third stock exchange, the Metropolitan Stock Exchange of India, widely referred to with its former acronym MCX, has negligible volumes.
"It was a matter of great concern," said Anupam Singhi, chief operating officer of financial firm William O'Neil India.
"The onus is now on NSE and how they look into such issues," he added. "This is an opportunity for BSE and MCX to create some business for themselves."
Others said the exchange needed to be better prepared for disruptions.
Reshmi Khurana, managing director at Kroll, said the NSE should respond by conducting a thorough investigation into what went wrong and work to prevent any recurrence including establishing a contingency plan and setting up a crisis team.
"The onus is on a company to respond to a crisis," she said. "Companies need to be more proactive than reactive in order to avoid getting caught out on similar crisis situations."
The NSE - owned by domestic financial institutions such as State Bank of India and units of foreign firms such as Citigroup Inc and Goldman Sachs Group Inc - is already under intense regulatory scrutiny.
Securities and Exchange Board of India Chairman Ajay Tyagi has said the regulator is seeking to appoint a forensic auditor to investigate whether NSE employees could have colluded with brokers to allow them early access to its brokers.
$1 = 64.5600 Indian rupees Additional reporting by Savio Shetty and Aby Jose Koilparambil; Editing by Jacqueline Wong, Robert Birsel