Obama said he wanted a congressional probe into the incidents, while Hillary Clinton's campaign said in a statement that she intended to "closely monitor" the State Department's investigation.
Two of the contract workers have been fired. The third has been disciplined, and the trainee has been "admonished."
The three contract workers were among 2,600 contract employees that the State Department uses to help an overburdened operation that last year turned out 18 million passports.
Officials declined to identify the firms employing the disciplined workers.
However, a Virginia firm, Stanley Inc., which holds several large government contracts, confirmed Friday that two employees of a subcontractor were involved in accessing Obama's passport records and were fired the day the unauthorized search took place.
Stanley officials said they didn't know whether any of their employees improperly snooped in files for McCain or Clinton.
"While this is a rare occurrence, we regret the unauthorized access of any individual's private information," the company said in a statement.
Stanley was awarded a new, $570-million passport contract this week; it also runs government facilities in Vermont, Arizona, Arkansas and California.
Its California contract is for work at a Laguna Niguel office that processes immigration and citizenship applications.
The State Department will try to determine whether the workers broke any laws and whether the supervisors broke any rules by failing to inform superiors of the incidents.
If the inspector general concludes that the breaches broke the law, State Department officials will ask the Justice Department to investigate.
State Department officials insisted the episode showed that their system for guarding against privacy violations had worked.
But they acknowledged that supervisors should have passed information about the infractions up the chain of command and said that rule changes are possible.
"We do feel like the system worked, but the system isn't perfect," State Department spokesman Sean McCormack said in his regular daily briefing.
Passport files contain basic information individuals must give the government to obtain a passport, including date of birth, address and Social Security number. They often contain information on family members, travel destinations and dates, and contact phone numbers.
