Fuchs, who was a reserve soldier in the Second Lebanon War, insists that Olmert resign immediately.
"When a prime minister in Israel fails so seriously in the state's most crucial test, he does not get an opportunity for a retake," he said.
'The report is harsh'
He also wrote in the petition that "while the judicial and political sagas continue, the citizens of the state find themselves in great embarrassment, not to say contained anger at the respondent (the prime minister) who is holding on 'for dear life,' stating that he has no intention of resigning.
"The entire public is held hostage in the hands of the respondent and can do nothing but appeal to this distinguished court."
The High Court rejected Fuchs' petition on Tuesday afternoon.
"The report is an interim report which was put on the government table yesterday, and is naturally still being studied by the concerned parties," the judges wrote in their decision.
In a televised address from his office, Olmert told the public Monday: "The report is harsh. Mistakes were made and major decision-makers, including myself, failed. We must draw conclusions and correct the many shortcomings; there is a lot to do. I intend to fix everything in need of fixing, quickly and thoroughly. It would be wrong to resign. It was this government that made the decisions and this government will engage in corrections."
The "battle" over the report's conclusions is entering the political arena full force Tuesday morning.
Among the political establishment, many are speculating whether the Labor Party will leave the coalition.
Associates of MK Ami Ayalon have told Ynet that if he wins the primaries, he will not consent to Labor staying in the government.