Damian Green must explain why half the immigration desks at Heathrow Airport were closed today despite long queues of passengers waiting to enter the country, a Labour MP said.
Keith Vaz, chairman of the Commons Home Affairs Select Committee, said he was appalled at the length of queues at 7am and that he would ask the Immigration Minister to explain the situation to MPs tomorrow.
His comments come just over two weeks before the Olympics start and after shadow home secretary Yvette Cooper said it was a disgrace that international athletes were waiting longer than two hours to pass through immigration control.
Mr Vaz said: "I was appalled by the length of queues in the immigration hall this morning.
"It is now two months since the Immigration Minister promised additional resources and better management.
"The worst aspect was that half of the immigration desks were simply not opened even though the Border Force had prior knowledge of all flight arrivals.
"This creates additional security pressures with luggage piling up in the baggage hall.
"We look forward to hearing the Immigration Minister's explanation for this tomorrow."
Queues at Heathrow Airport were more than an hour for non-EU passengers, despite a 45-minute target, when Mr Vaz visited Terminal 4 at 7am today, his spokeswoman said.
Yesterday, Ms Cooper said many of those forced to wait in long queues were Olympic athletes, who will be arriving ahead of the opening ceremony on July 27 to acclimatise to UK conditions.
A leaked memo reveals that tourists arriving from outside the European Economic Area are repeatedly waiting longer than the 45-minute target time to pass through passport control.
Meanwhile, European visitors are waiting longer than one hour when it should take less than 25 minutes to have their documents checked.
Ms Cooper accused Home Secretary Theresa May of failing to ensure enough staff were employed at peak times.
But Mr Green said the Government's actions to tackle queues "have resulted in real improvement over the last two months - including consistently hitting our targets on UK and EU passengers and reducing waiting times across the board".
"But we're not complacent about some long waiting times, which is why this weekend we have increased staffing numbers by more than 50% at Heathrow to respond to large passengers volumes," he said.
"And by the start of peak Olympic arrivals in less than 10 days, there will be up to 500 additional staff on our rotas across the country - this includes enough staff at Heathrow to cover every desk during busy times.
"Additionally we have special lanes in place designated to Olympic athletes to enable them to pass through the border without delay."
A spokesman for airport operator BAA said: "Immigration waiting times for passengers during peak periods at Heathrow in the last few days have been unacceptably long and the Home Office should be delivering a good experience for regular passengers as well as for Olympic visitors."
He went on: "Immigration is a matter for the Home Office.
"The Home Office has said that from July 15 all Border Force desks at Heathrow will be open during peak Olympic arrival periods."
Official figures showed the wait at immigration control for non-EU passengers this morning was 56 minutes.
A Border Force spokesman insisted Mr Vaz was incorrect.
"Queues at Terminal 4 remained under an hour at all times," he said.
"Staff were quickly redeployed and more than 80% of desks were open to process passengers as quickly as possible."
Later, Mr Vaz urged ministers to inspect Heathrow at peak times.
"I was there at 7am this morning," he told the Commons.
"I was appalled to see people being held in corridors, an immigration hall was full as well as half the kiosks not being opened.
"Could we please start the additional measures for the Olympics immediately?"
Mrs May said ministers visited Heathrow at various times to understand the different circumstances and the extra workers for the Games would start in a week.
She told Mr Vaz: "At Terminal Four today queues were not over an hour as I understand you said they were.
"Staff were being quickly redeployed and more than 80% of desks were open to process passengers as quickly as possible."