"There is sufficient evidence indicating that in several cases ... the president carried out acts of rape, forced sexual acts, sexual acts without consent and sexual harassment," the Israeli police said in a statement.
The recommendation was made during a meeting between police investigators and Meni Mazuz, the Israeli attorney general, who will decided whether the president should face trial.
According to the statement, the police also believe that there is enough evidence to bring charges of fraud and malfeasance in office over the granting of pardons by the president, as well as charges for carrying out illegal wire-taps.
Accusations that Katsav disrupted a police investigation and harassed a witness are still being investigated.
The charges would be the most serious ever brought against a serving Israeli official and Katsav is immune from standing trial unless he is impeached by parliament.
Katsav has denied any wrongdoing and said he has been the victim of a "public lynching without trial or investigation".
Israel Radio and Channel 2 TV said the case against the president is based on complaints by five women who claimed he made unwanted sexual advances toward them during his time as president and before that, when he was a government minister.
Complaints by five other women are not being pursued because the statute of limitations has run out, media reports said.
A police investigation was launched earlier this year after a former employee alleged he forced her to have sex under the threat of dismissal.
Police have repeatedly questioned Katsav at his official residence as well as seizing his computer and personal documents.
The position of president in Israel is largely ceremonial and carries very little real authority.