More than 430 women have been wrongly excluded from the programme since 1997 after having a partial hysterectomy, the minister told MSPs on Thursday.
One of these women has since died of cervical cancer.
A routine audit of cervical cancer data discovered in December last year that some women who should have been invited for screening had not been, as only those who have had a full hysterectomy should be excluded.
Speaking to BBC Good Morning Scotland on Friday, Ms Todd said the true figure of those affected “may be higher”.
She said: "I'm afraid we may well be looking at higher numbers."
The records of at least 500 women who had partial hysterectomies before 1997 still need to be checked, Ms Todd said.
These are more difficult to access, but should be checked before the end of July.
Ms Todd said the NHS would review the records of all women who had been excluded because of a hysterectomy – some 200,000 people – as a “precaution".
But she “fully expects” there to be no further errors among this group.
Opposition MSPs have questioned the delay between ministers learning of the issue and it being announced to the public.
Labour’s Jackie Baillie said: “The SNP’s decision to keep the public in the dark on such a serious mistake beggars belief.
“These women were failed for decades. The least they deserve is to have been made aware of the risk facing them as soon as it came to light.”
The Scottish Conservatives’ Annie Wells said: “SNP ministers have serious questions to answer as to how urgently they addressed this issue.
"They were first made aware of these errors in March well before Parliament shut down for the election, but only started sending out letters to women this week. That is simply not good enough.
“Their current mixed messaging over why they didn’t contact women immediately is also extremely unhelpful, especially now that they have confirmed further records are being checked.”