A blunder by the UK's most senior counter-terror officer did not damage an operation to thwart a suspected bomb plot, Jacqui Smith has said.
The home secretary told MPs the only impact had been that raids had been brought forward "by a matter of hours".
Assistant Commissioner Bob Quick quit on 9 April after accidentally revealing operational details to photographers.
Shadow home secretary Chris Grayling called the incident another "chapter of chaos" in the Home Office.
Twelve men were arrested in raids in Manchester, Liverpool and Lancashire on 8 April as part of the operation.
Last week officers were given more time to question 11 of those men, 10 of whom are Pakistan nationals. The other is from Britain.
An 18-year-old has been released into the custody of the UK Border Agency.
In a statement to the House of Commons on Monday, Ms Smith told MPs the operation had not been jeopardised by Mr Quick's act of accidently revealing a secret document he was carrying when arriving at a Downing Street briefing.
The emergence of a terror threat within the UK from this [student visa] system is a worrying... new development
Shadow home secretary
"The fact that these papers were inadvertently made public did not make any difference to the decision to carry out arrests - it simply changed the timing by a matter of hours," she said.
Ms Smith did not confirm reports that most of those arrested had been on student visas, but said the visa system had been tightened up.
Fingerprints were now checked against counter-terrorism and crime databases as well as UK border agency records, she said.
"In posts that we've classified as high risk, like Pakistan, we have a risk management network that helps ensure the right visa decisions are made - for example, by working with local authorities to ensure that the qualifications of prospective students are independently verified.
"The impact of these changes is demonstrated in the increased refusal rate for visa applications from Pakistan nationals."
Searches 'near end'
The number of institutions registered to bring in international students had also fallen from around 4,000 to 1,500, she said.
She added that the Security Industry Authority, which issues licences to people working in private security, had been asked to review whether its processes needed to be strengthened.
Mr Grayling congratulated the police for acting promptly after Mr Quick's security breach, but said the events of the last few weeks amounted to "another chapter of chaos in the Home Office".
"We have warned for years about abuses of the student visa system for immigration purposes," he told MPs.
The 'secret' documents clutched by Mr Quick were clearly on show
"But the emergence of a terror threat within the UK from this system is a worrying, though perhaps, unsurprising, new development."
He also argued new control procedures would not protect the UK from people previously unknown as terrorists.
Manchester's counter-terrorism unit said most of the searches relating to the terror arrests had been completed and material collected was now being assessed.
"As this complex and detailed investigation continues, officers are sifting through the extensive amount of information so far received to assess its relevance to the investigation," a spokesman said.
"This is a time-consuming process, and we remain grateful to the local communities affected for their continuing co-operation and support."
Meanwhile, the Home Office has announced an extra £5 million of funding to pay for measures to protect crowded public places from terrorist attack.
Security minister Lord West said the cash would available to local authorities and other bodies to combat the "severe" threat posed by terrorism.
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