In an opinion piece to be published in Sunday's Inquirer, Williams said that the "vast majority" of the withdrawals made sense, but that he regretted some and would reverse them.
"Unfortunately, in a handful of cases, some genuinely serious charges slipped through and were mistakenly dismissed along with the others," he wrote. He said the charges in those cases had been miscoded by the courts and withdrawn by his office in error.
"We didn't catch the errors," he wrote.
The withdrawals, which required judicial approval, created a furor, with critics saying the move delivered a message that it paid for criminals to run. Since the news broke, the District Attorney's Office also has been busy fielding calls from defendants from years past, wondering about the status of their cases.
Williams invited victims of all the purged cases to contact his office if they believed the crimes could be successfully prosecuted.
"These dismissals are not permanent," he wrote. "We can and will ask the court to reinstate charges that should never have been withdrawn."
Carol Lavery, the state's victim advocate, said Friday she was encouraged by Williams' change of heart.
"I'm very glad to hear they've rethought this process," she said. "I think that's very good for victims."
Still, at least one victim said she had changed her mind about pursuing her case.
The woman, who was sexually assaulted at gunpoint in 1987, told The Inquirer last week she was eager to see her assailant stand trial. On Friday, she said she was no longer so sure.
"I don't want to bring back memories," the woman said through a Spanish interpreter. "I just want to get on with my life."
In a sweeping move to lower Philadelphia's massive fugitive tally, Williams and Pennsylvania Chief Justice Ronald D. Castille urged the city's top judges to close criminal cases and cancel bench warrants for thousands of defendants in cases dating to 1998 and earlier.