Mr Green made an emergency Commons statement on the lengthy immigration queues seen at Heathrow recently.
He said delays were caused mainly by severe weather disrupting flights.
But shadow immigration minister Chris Bryant said the problem was down to a lack of resources and the government was “running out of alibis”.
Speaker John Bercow granted an urgent question to Commons Home Affairs Committee chairman Keith Vaz.
Mr Green acknowledged that the queues at passport control at Heathrow over the weekend were unacceptable.
Non-EU nationals were waiting up to 90 minutes at Heathrow’s Terminal 5 on Friday night.
But Mr Green insisted that in general waiting times for passengers were meeting the agreed targets.
He outlined the measures he was taking to solve the problem, particularly during the run-up to the Olympics.
He said: “Border Force will ensure that all immigration desks at Heathrow and other key ports and airports in the South East are fully staffed during peak periods over the summer.
Air traveller Kevin Quinn said there was “absolute carnage” at Heathrow Terminal 5 on Monday
“A contingency force of appropriately trained staff will be sent to the border to provide extra help to ensure passengers are processed as quickly as possible.
“Border security is Britain’s first line of defence. It cannot and will not be compromised.”
Mr Green said the vast majority of people passed through immigration control “quickly”.
Between January and March the average waiting time was six minutes for UK and EU citizens and 25 minutes for non-EU passengers, he added.
And he said that, in the first two weeks of April, 99% of UK and other EU nationals got through within the force’s 25-minute target.
But Willie Walsh, chief executive of British Airways’ parent company IAG, said that claim “was based on a sample size of less than 0.2%”.
It takes some time to move from terminal to terminal at Heathrow. So even then deployment isn’t going to be an instantaneous thing as Mr Green thinks it is”
Lucy Moreton, Immigration Services Union
In any case, that target was “pathetic and undemanding”, he said, adding: “The equivalent target for critical security checks is five minutes.”
He added: “We need a full and permanent solution urgently, and a greater sense that the scale of the issue is understood in Whitehall.”
Mr Green also said there would be a new Border Force central control room at Heathrow and rapid response teams to deal with pressures across the airport, and new shift patterns would be implemented within weeks.
But the Immigration Services Union’s Lucy Moreton told BBC News: “It takes some time to move from terminal to terminal at Heathrow – it takes about 45 minutes to get to each side of the airport.
“So even then deployment isn’t going to be an instantaneous thing as Mr Green thinks it is.”
She criticised him for talking of “an unexpected surge in passenger flows” and said: “These aircraft have been flying for some hours and we do know exactly how many people are on them.
“And we know exactly when they’re going to come in to land because, if we didn’t, they’d bump into each other.”
Labour said there were 107 breaches of maximum waiting time targets in the first half of April.
I had read about the queues in the paper before I came back but I didn’t think they were this bad”
Passenger Kevin Quinn
Mr Bryant said: “The government is running out of alibis. These figures show the government hasn’t given the Border Force enough resources to do the job properly and is displaying utter incompetence.”
Mr Vaz said the long queues were a “serious embarrassment” to the country.
He said there were reports of unmanned desks at immigration during peak times and iris scanners that were broken.
Mr Vaz said doing nothing about the problem was “simply not acceptable” during this summer’s Olympics and beyond.
Passenger Kevin Quinn, from Sutton, south London, said there was “absolute carnage” in Heathrow’s Terminal 5 when he returned from Hamburg on Monday.
He told the BBC: “I had read about the queues in the paper before I came back but I didn’t think they were this bad.”
Meanwhile, a “furious row” has broken out between Heathrow owner BAA and the Home Office, sources have told the BBC’s home affairs correspondent Tom Symonds
The Home Office is angry that emails to BAA about leaflets given out by the airport – telling passengers to complain to the Home Office – were leaked to the Daily Telegraph, the sources said.
They said the issue had led to shouting match on the phone between a BAA executive and a Home Office official.
The BBC has also seen confidential leaked UK Border figures which show a fall in the number of forged documents detected in the past three months.
Passenger Leo Lourdes says it was the longest queue he had ever seen
They show 6.5% fewer detections recorded in January than in the same month in 2011, 26% fewer year-on-year in February, and 16% fewer in March.
A Heathrow passport control officer, who spoke to the BBC anonymously, said he was “absolutely certain” detection rates had fallen partly as a result of staff shortages.
The fall showed staff were under so much pressure they were unable to closely question the holders of potentially forged passports, the passport control officer said.
But the BBC’s Tom Symonds said the number of detections had also fallen because of the introduction of British passport checks abroad and because the new biometric passport is harder to forge.
The Home Office is aware the detection figures have been leaked but has made no comment so far.
The UK Border Force does not publish its queue monitoring data publicly while the BBC understands BAA Heathrow is planning to start publishing its own figures on Friday or next Monday.
London Mayor Boris Johnson has voiced his “serious concern” at the delays.
The prime minister’s official spokesman said the Border Force was working on the problems after non-EU passengers spoke of three-hour queues last week.
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