Newly-appointed Home Secretary Sajid Javid gave an update on the work of the dedicated taskforce set up last month to help those affected by the scandal.
Mr Javid told the Commons: “Each person that is identified as potentially from the Windrush generation is called back by an experienced and sympathetic case worker, who then helps them through the process.”
Since it was established last month by his predecessor Amber Rudd, the team has received more than 7,000 calls.
Of those, 3,000 have been identified as “potential Windrush cases”, Mr Javid said.
This has increased from 2,500 when the last update was provided on Monday.
People in this group are invited to service centres around the country for appointments, with travel costs reimbursed by the UK Government.
So far, more than 700 appointments have been scheduled and more than 100 people have had their cases processed and now have the documents they need, the Home Secretary told MPs.
He said: “These numbers are increasing by the day and we will continue to schedule these appointments as a matter of urgency.”
Mr Javid also emphasised any information provided to the taskforce would be used for no other immigration purpose than helping people confirm their status.
Theresa May has meanwhile said a review of the Windrush generation scandal would have “full access” to Home Office information, ahead of a Labour move to force disclosure of internal documents.
The Prime Minister, who was home secretary before entering Number 10, promised a “package of measures to bring transparency on the issue”.
Labour hopes to use a parliamentary procedure to force ministers to hand over correspondence, including text messages and emails, between ministers, officials and special advisers between May 2010 and this year.
At Prime Minister’s Questions today, Mrs May said Mr Javid would set out the actions being taken by the Government on the issue.
She said “speed is of the essence” and Mr Javid “will be commissioning a full review of lessons learned, independent oversight and external challenge with the intention of reporting back to this House before we rise for the summer”.
The review will have “full access to all relevant information in the Home Office, including policy papers and casework decisions”.
Shadow home secretary Diane Abbott said the scandal had “exposed something rotten at the heart of Government” and “full disclosure of the facts” was required.
The Tories are expected to oppose Labour’s motion, which would see the internal documents handed to the Home Affairs Committee.
The rarely-used procedure, called a “motion for a return”, involves asking the Queen to direct her ministers to provide the requested documents.
Ms Abbott said: “With the resignation of Amber Rudd, Theresa May has lost her human shield and must now fully account for the policies she created and drove through from the Home Office into Downing Street.
“The Windrush scandal has exposed something rotten at the heart of Government. We need to know what has led to this situation.”