The first round of elections took place on October 25 and involved 54 candidates. Celestin suggested he might boycott the second round if the initial voter tally was not reviewed.
International observers, led by the Organization of American States (OAS), which monitors elections across Latin America, acknowledged some voting irregularities, but had initially sanctioned the first round of voting.
But eight presidential candidates called for an investigation into voting that put Moise in the lead with 32 percent of the vote.
Under mounting pressure from increased street protests, Martelly ordered the creation of a special commission to assess Haiti's electoral process, and said the commission would draw assistance from the OAS and European Union voting experts.
Monday’s announcement also comes less than one month from the sixth anniversary of a 7.0 earthquake that rocked the Haitian capital, leaving at least 200,000 people dead and 1.5 million displaced.
More than 60,000 people remain internally displaced, and living in tents, according to recent estimates by the United Nations Stabilization Mission in Haiti.
Al Jazeera’s Etant Dupain contributed to this report from Port au Prince, Haiti