Some 20,000 people rallied in Tel Aviv on Saturday against the deal struck with Attorney General Menachem Mazuz.
Under the bargain, he was due to be charged with lesser sexual offences and faced a suspended sentence.
Now Mr Mazuz, who earlier said evidence of rape was not "sufficiently solid", has 24 hours to justify his decision.
"It's a deal that stains us all, we should not agree to let this sully our society"
Rape convictions in Israel carry a maximum sentence of 16 years in prison.
Mr Katsav finally resigned as president on Sunday. Former Prime Minister Shimon Peres will replace him formally on 15 July.
Under the plea bargain signed on Thursday, he admits to sexual harassment and indecent acts but two rape counts included in the original charge sheet have been dropped.
Society 'sullied'
Michael Partem, vice-chairman of the Movement for Quality Government in Israel group, said the plea bargain had to be voided.
"Instead of prosecuting the president as an ordinary person and applying the rule of law equally, it goes easy on the president... it's been reduced to a slap on the wrist," he said.
Women's groups and victims of sex attacks led the protest against the attorney general's decision to drop rape charges against Mr Katsav.
"It's a deal that stains us all, we should not agree to let this sully our society," Education Minister Yuli Tamir told the crowd on Rabin Square.
Correspondents say the turnout for the rally was the highest in years for a women's rights protest in Israel.
There have long been complaints that the authorities do little to counter sexual harassment at work.
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