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.
More than four hundred people have visited a health centre for screening for blood-borne viruses after 22,000 dental patients were recalled.