Nottinghamshire dentist Desmond D'Mello has been suspended by the General Dental Council over serious hygiene concerns.
Patients are being offered tests for HIV and hepatitis.
Doug Black, medical director for NHS England in Nottinghamshire, said it was the "largest recall in NHS history".
He said: "We are doing our level best to meet demand, but to avoid waiting, people can book an appointment for another time and come back."
Mr Black said it was important people attended the Highcroft Medical Centre, in Arnold, rather than going elsewhere.
"The samples we are taking are being sent to a dedicated laboratory, which enables us to track the results," he added.
The death of a woman treated at the practice in Daybrook, Nottinghamshire is also being investigated by police.
Amy Duffield died in August 2013 shortly after being treated by the dentist.
NHS England said it appeared Mr D'Mello failed to wash his hands and used the same instruments for more than one patient without sterilising them between appointments.
Experts said the risk of infection was believed to be low and Mr D'Mello had been tested and was clear of all diseases.
A Care Quality Commission inspection in July also raised concerns about the possibility of cross-contamination at the practice.
However, inspectors who had visited the clinic in November last year, gave it a clean bill of health.
The new owners of the practice have renovated the property and addressed all the concerns, the inspectors said.
Nottinghamshire Police was asked by the coroner to investigate Miss Duffield's death.
Miss Duffield, a Leeds University graduate, died in hospital in August 2013 of viral acute myocarditis after suffering palpitations, her family said.
Her mother Sharon Duffield said: "We will of course be interested in the findings of the investigation, whatever the outcome, but it won't bring Amy back."
Test results are expected to be available in 14 days.

Axis Studios has secured Scottish Enterprise backing to take on 20 additional staff.
The company works for major studios on animations and special visual effects in TV and film drama.
It said it was on course to triple turnover between 2015 and 2018 to Â£15m, working from bases in Glasgow, Bristol and London.
Axis Studios was founded in 2000, and has recently worked for Netflix, Warner Bros, the BBC, Sega and Universal Studios.

Norfolk-based Gardline, founded by the Darling family in 1969, employs 750 people and has been bought by Dutch firm, Royal Boskalis Westminster.
Gardline's activities include marine geophysical surveys, offshore geotechnical services and environmental surveys.
Boskalis has taken on the firm's assumed debt as part of the deal.
In a joint statement, the firms said there were "significant synergies" between them.
Gardline operates 40 vessels, including crew transfer ships and survey catamarans.
Its head offices are in Great Yarmouth, with further activities in the USA, Brazil and Singapore.
Boskalis has a fleet of more than 900 vessels and floating equipment and 11,700 employees, operating in more than 90 countries across six continents.
"With the acquisition, Boskalis strengthens its position as marine services provider in north-west Europe," it said.
Gardline's profits have fallen in recent years, and Boskalis said the company had suffered from the downturn in oil and gas.
It said it was not forecasting Gardline's finances would be turned around in the short-term but that the acquisition "positions Boskalis well for when end-markets recover".
Earlier this month, Gardline secured contracts worth £6m with Scottish Power Renewables to carry out a range of pre-construction surveys across East Anglia offshore wind farm sites.
Boskalis has yet to respond to questions on whether jobs will be affected by the takeover.
More than four hundred people have visited a health centre for screening for blood-borne viruses after 22,000 dental patients were recalled.
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