Home Secretary Theresa May has told MPs she will not resign over revelations that UK border checks were relaxed over a four month period.
She said UK Border Force boss Brodie Clark must take responsibility for his "unauthorised actions".
Mrs May allowed some checks on European travellers to be relaxed but says Mr Clark went further in scaling back checks, without her approval.
Labour say it is "shocking" she cannot say how many airports relaxed checks.
It is understood Mr Clark is discussing his position with union officials from the First Division Association, which represents senior civil servants.
Questioned about the row by MPs on the Commons home affairs committee, Mrs May said she had not told the Cabinet of her decision to allow officials to relax checks on some European travellers arriving in the UK.
The "limited" pilot was an "operational matter", she said, which "did not in any way put border security at risk".
The idea was that at busy times, it was safer to carry out "intelligence-led" checks on suspicious passengers rather than mandatory checks on all passengers, including those who were "low risk", she said.
Labour committee member David Winnick told her that the relaxation of controls meant that "presumably thousands" of people had been allowed in to the UK who "may well have been stopped if the proper procedures" had been stuck to.
He suggested ministers should take full responsibility for a "major blunder" on their watch and asked if there was any question of Mrs May resigning - to which the home secretary responded: "No."
Mrs May said there were other procedures which prevented people from arriving illegally in the UK - including the e-Borders programme and the identification of potential threats by UK officers overseas.
She said she would take responsibility for the authorised pilot - which she suggested had led to a 10% increase in the detection of illegal immigrants - but Mr Clark must "take full responsibility for his actions".
Mrs May said the pilot scheme had been made available across all ports but was "not necessarily used at all ports" - where exactly they had been used would be determined by the inquiries she had authorised.
She was asked about a paragraph in a leaked document from the UKBA, entitled "Trial of risk based processes at the border" and dated 28 July, which suggested that "if for whatever reason it is considered necessary to take further measures, beyond those listed above, local managers must escalate to the Border Force Duty Director to seek authority for their proposed action".
Mrs May said that paragraph related to health and safety concerns dating back to 2007 - where there were so many people queuing that there were safety concerns for them - that allowed officers to go to "level two checks" - similar to those authorised by her pilot - to ease the crush.
Giving evidence to the liaison committee of senior MPs, Prime Minister David Cameron said there had been "activity going on by the UK Border Agency that was not acceptable".
But Labour shadow home secretary Yvette Cooper said it was "shocking" Mrs May was unable to say how many airports had relaxed checks over the summer - even under her own pilot scheme, which she authorised.
She said Mrs May should publish the guidance given to the UK Borders Agency and what information it provided to the Home Office.
"There is still a massive gap between what the home secretary is saying and what the guidance going out to Border Agency staff, even on her own so-called pilot, actually said," Ms Cooper said.
"It's a deep concern that what we have got is the home secretary blaming the officials a lot but still not being able to provide us with answers to the questions she should have asked."
Brodie Clark, head of the UK Border Force, is among three staff suspended. Mrs May has announced there will be three inquiries, the main one led by the Chief Inspector of the UK Border Agency, John Vine.
Mr Clark and Rob Whiteman, the UKBA chief executive, are to be called in front of the home affairs committee to answer questions about the matter.
The home secretary has said the pilot scheme she authorised was to be used "under limited circumstances". It allowed border officials to use discretion to judge when to open the biometric chip on the passports of people from within the European Union, to check a second secure photograph.
Checks were also relaxed on children from the EU who were travelling with their parents or as part of a school group, under "limited circumstances".
However Mrs May said biometric checks on European nationals and warnings index checks on children from the EU "were abandoned on a regular basis" and the same checks on people from outside the European Economic Area (EEA) "are also thought to have been abandoned on occasions".
Mrs May added that adults were not checked against the "warnings index" watch list at Calais, and also that fingerprinting of people from outside the European Economic Area who required a visa, was stopped.
Downing Street defended Mrs May's decision to pilot the relaxation of or border controls for EU nationals, calling it a "sensible thing to do" but Labour has accused her of giving "the green light for weaker controls".
Labour and unions have claimed that staff shortages - due to cuts to the UKBA - are at the root of the problems.
Some 5,000 posts are due to go by 2015 as part of wider government cost-saving measures.