Priti Patel told MPs there would be “no formal end date” for applications to the Windrush compensation scheme.
It means eligible claimants can continue to apply after April 2023, when the scheme was previously due to end.
Speaking to the Commons Home Affairs Committee Ms Patel said: “I’m announcing that there will be no formal end date for the scheme and this is to ensure that anyone, absolutely anyone who was affected by the terrible injustices of Windrush, receives the compensation that they deserve.”
So far the department has offered more than £34 million in payouts, of which almost £27 million has already been awarded.
Committee member Diane Abbott said 110,000 people had signed a petition calling for the compensation scheme to be moved out of Home Office control and be overseen by an independent body instead, adding: “Because one of the reasons why the numbers of people applying for compensation have been so low is that people do not trust the Home Office.”
She asked: “Are you willing to consider moving the actual compensation scheme to an independent body?”
Ms Patel replied: “I do not think a structural reform of the scheme or moving it elsewhere will necessarily increase the number of applicants or claimants coming forward.”
She reiterated the efforts already made to overhaul and improve the scheme and the “significant” amount of money which has already been offered to victims.
Trust will “not be rebuilt overnight” but the department is working in an “engaging way” in “every way possible to build links within the communities to regain trust and support”, Ms Patel added.
The Home Office initially estimated it would receive around 15,000 eligible claims, but so far 2,631 have been submitted.
As a result it has lowered the number of claims it is expected to receive to a range of 4,000 to 6,000 but the department insisted there is not a cap on the number of people who can apply or be considered for compensation and there is not limit on the total amount the department will pay out.
When questioned about this, Ms Patel said: “It’s very difficult to estimate the volumes of eligible claims that are likely to be received and that is a challenging task.”
Figures published on Thursday show that, to the end of June, the Home Office paid £26.9million to 776 people and offered a further £7.3 million.
Some 163 claims were for people who had already died, but only five have resulted in payments so far.
Other changes made to the scheme intend to make it easier for those claiming on behalf of a relative who has already died, according to the Home Office.
Appeals have been made against decisions in more than 200 cases, while 294 eligible applicants were told they were not entitled to any money because their claims did not demonstrate they had been adversely affected by the scandal.
There have been 125 claims rejected on eligibility grounds.
Victims were promised bigger, quicker payouts following complaints of difficulties in claiming compensation as part of an overhaul of the scheme in December.
Earlier this year, Whitehall’s spending watchdog, the National Audit Office (NAO), found Windrush victims were still facing long waits to receive compensation and concluded the scheme it yet to meet its objective of paying out to those affected quickly.
When the scheme launched, it had just six full-time equivalent caseworkers compared to the 200 the department said it needed from the outset, the report found.
It is understood more caseworkers have since been hired and trained.
The scandal erupted in 2018 when British citizens, mostly from the Caribbean, were wrongly detained, deported or threatened with deportation, despite having the right to live in Britain.
Many lost homes and jobs and were denied access to healthcare and benefits.