"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," police said in a statement Sunday.
"There is sufficient evidence indicating violation of the law banning wire-tapping by the president," they said following a meeting with investigators and Attorney General Menachem Mazuz.
Katsav had originally said that he would preside over the opening of the Knesset's winter session despite the police statement, but later cancelled his appearance after a wave of protests from lawmakers.
"President Katsav has announced that he has thanked parliament speaker Dalia Yitzik for her invitation to attend the opening session, but in view of the current circumstances, he preferred to decline the invitation," public radio reported.
Katsav is immune from prosecution while holder of the largely ceremonial role president, but he could be charged if impeached by the Knesset.
The attorney general is expected to decide within two to three weeks whether to file an indictment against Katsav, a married father of five who has denied the allegations against him and says he is the victim of a "witchhunt."
Katsav, 60, has rejected calls that he step down pending the investigation and could face between three and 16 years in prison if convicted, Israeli radio reported.
"Police have no legal authority to make any recommendations of this type," said Katsav's attorney Zion Amir.
"This is not the first time police have recommended the indictment of senior figures, including prime ministers, and those recommendations have all been rejected," he said.
In recent weeks, police have investigated no fewer than 10 complaints of rape and sexual harassment by former Katsav employees during his presidency and as tourism minister.
The Iranian-born president has been questioned by police five times over allegations that he forced women employees to have sex with him by abusing his position of authority.
Police sources now say that an indictment could be filed in three or four of these cases.
Katsav, a member of the right-wing Likud party, was elected president by MPs in July 2000 as a relative outsider who upset frontrunner Shimon Peres, an ex-premier and Nobel peace laureate.