The Treasury Committee requested that RBS chief executive Stephen Hester provide a detailed explanation of what went wrong at the bank to cause its ongoing IT issues.
In a letter to the bank, Andrew Tyrie, chairman of the Treasury Committee asked for preliminary answers to be provided by the end of this week, and a more detailed report by the end of next week unless the bank was "still fire fighting".
"The Treasury Committee is extremely concerned about the current crisis at RBS.
"Your first priority must be to resolve this crisis, caused by the failure of your computer systems. We would appreciate a report on how close you are to achieving this, both in the UK and for your operations in Ireland. We would like this by the end of the week," Tyrie wrote.
An upgrade made to batch processing software CA 7 from CA Technologies is believed to be at the heart of the IT failure, which has affected 17 million customers of the Royal Bank of Scotland, NatWest and Ulster Bank.
Usually, if a software update from a vendor causes a problem, the customer can back out of an upgrade. However in doing so, a junior RBS IT worker based in India reportedly made a major mistake by deleting all the scheduling that was in place, which meant that the information had to be re-inputted into the system, according to The Register.
The reduction of UK IT staff and an increase of outsourcing of IT to India has been cited by media reports as the reason behind RBS's problems, and in its detailed report to the MPs, the bank will have to explain whether staff savings or IT outsourcing did indeed contribute to the problems. Chief executive Hester has denied that outsourcing was a root cause.
Meanwhile, the bank will need to review its risk identification and contingency plans, as well as reveal what assessment it has made of the "enduring risk" to its computer systems.
Tyrie has also written to the Financial Services Authority (FSA) asking it to set out its plans for investigating the RBS case, and what action the regulator has been taking to ensure proper oversight of banks' computer systems.
"This is the latest in a series of computer failures to have affected bank customers," said Tyrie.
"We need to know exactly what went wrong and what will be done to give us confidence that similar mistakes are not repeated in the future."
It has been more than a week since the RBS meltdown occured on 19 June, with bank branches continuing to stay open for longer hours this week to deal with customer enquiries.