"On this day I urge everyone to work in the spirit of tolerance, mutual accommodation and respect for dissent and invite everyone to participate in the national effort for ... reconciliation and healing the wounds," Zardari said.
Chaudhry was removed in 2007 by Pervez Musharraf, the former president, after he began examining cases that could have threatened Musharraf's legitimacy as he sought a new term in office.
Zardari agreed last week to reinstate the chief justice, after activist lawyers and opposition supporters began a march towards Islamabad, the capital, where they planned to stage an indefinite sit-in at parliament.
Zardari's address on Monday marked a break from months of bitter political wrangling over Chaudhry's reinstatement.
Despite the easing of political tension, the country's security crisis showed no sign of improvement.
Zeina Khodr, Al Jazeera's correspondent in Islamabad, said most Pakistanis want the feuding parties to resolve their differences so that security issues can be resolved.
She said Pakistani authorities cancelled the annual military parade and other ceremonies on Monday because of security concerns.
Republic day commemorates a 1940 resolution that led to Pakistan's statehood.