On Monday, Theresa May admitted she had authorised officials to relax security procedures on some European travellers coming into the country.
But she said checks on non-EU nationals were then scaled back further, without ministerial approval.
Labour has accused her of giving "the green light for weaker controls".
Mrs May has ordered an inquiry into the claims identity checks on travellers from outside Europe were scaled back in the summer, beyond what ministers had agreed in a pilot scheme.
In a statement to MPs on Monday, Mrs May said those responsible would be punished. Brodie Clark, head of the UK Border Force, is among three staff suspended.
The home secretary has said she does not know how many people have entered the UK without proper checks.
Pilot schemeBBC News Channel chief political correspondent Norman Smith said she faced questions about her competence - as she appeared to be unaware that the UK Border Agency (UKBA) was operating a more liberal approach towards non-EU travellers for four months.He also said Labour were pressing for more details of a Home Office "away day" with officials from the UK Border Agency which took place nine days before checks were relaxed.
Mrs May had been due to speak to the Commons home affairs committee on Tuesday about the new National Crime Agency and the summer riots.
But committee chairman Keith Vaz said he now wanted to know whether the pilot scheme to relax some checks was monitored and whether immigration ministers had met with senior UKBA officials during the scheme.
Speaking to BBC Radio 4's Today programme, Labour MP Alun Michael, who is on the committee, said he wanted more details about the pilot scheme she had authorised and who knew about it.
He said: "We have the head of the Border Agency into the home affairs select committee every three months.
"That's very unusual and the reason is because we've been very unsatisfied month after month with the replies that we've got on all sorts of issues. So this comes on top of the fact that the home secretary knew of the deep concern of members of Parliament about the Border Agency in all aspects of its work."
The home secretary has said the pilot scheme was to be used "under limited circumstances" at times when the volume of passengers was such that more "risk-based checks" would strengthen border security.
Under the scheme agreed by ministers, border officials were allowed 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 would also be relaxed on children from the EU who were travelling with their parents or as part of a school group.
'Abandoned'However, Mrs May said the relaxing of checks had gone beyond what she had authorised - without ministerial approval.
She 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.
In a note sent to regional directors last Thursday, seen by the BBC, UKBA chief executive Rob Whiteman ruled there could be no deviation from full immigration checks without his personal authorisation and announced the "immediate cessation" of the pilot scheme.
He demanded a return to "full and complete" warning index checks on all passengers, and required biometric checks on visa holders to be conducted fully at ports where they are used.
Mrs May has announced there will be three inquiries, the main one led by the Chief Inspector of the UK Border Agency, John Vine.
No 10 has said the prime minister has "full confidence" in the home secretary.
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.
Shadow home secretary Yvette Cooper accused Mrs May of presiding over "growing chaos and corner-cutting at our borders" and urged her to "get a grip".
