The Home Secretary must explain her "cover-up" of a "deeply worrying breakdown" of e-Border controls, Labour has said.
The Government has admitted that the e-Border control system failed over June 14 and 15 last year but said other checks remained in place.
Shadow commons leader Chris Bryant said Theresa May should explain the breakdown to MPs and whether further failures have happened.
Speaking during the business statement in the House of Commons, he said: "Can we have a statement from the Home Secretary on the deeply worrying breakdown of the e-Borders system on the 14 and 15 of June Last year?
"We need to know firstly, have there been other breakdowns, were full Warnings Index checks implemented and, above all, why did the Home Secretary cover this up for so long?"
He warned Commons Leader and Brexit campaigner Chris Grayling that the real threat to the UK's borders was "Tory incompetence".
"You say we should leave the EU so we can control our borders, but surely the lesson we should learn is that the greatest threat to our borders is frankly Tory incompetence," he said.
Mr Grayling said: "When Labour were in power the e-Borders programme was supposed to arrive and be put in to affect and it wasn't and it didn't happen because they failed to deliver the programme.
"So when they talk to us about what we've done in Government, they were in power for 13 years. They started by dismantling our exit checks of borders and they completely failed to put in place an alternative."
Downing Street said the Government was not disputing the fact that the Semaphore system had gone down, but said that it was only one of several layers of checks on people travelling to the UK.
Even while Semaphore was down, the authorities were "able to maintain full checks on 100% of arriving passengers", she said.
"We have a multi-layered approach to ensure that we have the toughest security possible at our border," said the spokeswoman.
"Semaphore is entirely separate - that allows us to do advance checks, but we then have the Warnings Index system in place and those are conducted at the border irrespective of any information received through Semaphore."