On Tuesday, a religious feminist organisation appealed to the high court against Ramon's nomination, branding it "amoral" and "unacceptable".
The government has faced a series of probes implicating Olmert and his lieutenants - the latest was the case of Avraham Hirshson, the finance minister, who resigned over the weekend amid police inquiries for embezzlement.
Ramon had resigned as justice minister last August, after he was accused of forcibly kissing a soldier at a party on July 12 - the day Israel launched its devastating war against Lebanon's Hezbollah.
Though he denied the charges, a court later convicted him.
Ramon helped found Kadima with Ariel Sharon, the former Israeli premier, and is considered one of the closest allies of the beleaguered premier.