Up to now, the city has held nonpartisan elections in May.
"Just having nonpartisan elections alone is not the way to do this."
The 53-year-old Democrat received 64 percent of the vote in the nonpartisan election.
The issue of nonpartisan elections has been debated throughout the city since last year.
Mayor Giuliani will then be required by law to call a nonpartisan special election within 60 days.
Council members are elected in nonpartisan elections and serve four year terms.
Most major American cities elect their local officials through nonpartisan elections.
The nonpartisan election, to be held on Tuesday, has drawn regional attention.
The nonpartisan municipal preliminary election was held on September 23, 1975.
At the same time, nonpartisan elections need not diminish the influence of political parties.