First mayoralty (1985–1993)
Suarez was first elected Mayor of Miami after running again in 1985, unseating Ferré. Suarez was re-elected in 1987 (fending off challenges from Ferré and Marvin Dunn). He was elected for a third term in 1989, with this third election being for a four-year term.
Suarez was sworn in as mayor on November 13, 1985, succeeding Ferré. He was the first Cuban-born individual serve as the city's mayor.
As mayor, Suarez was famous for keeping blue slips of paper in an office binder on which he recorded neighborhood concerns that had been brought to his attention by individual residents. This included concerns as small and local as an individual pothole. A joke arose in Miami politics that, as mayor, Suarez was more akin to a great public works director.
Suarez (at the time a political independent) endorsed the successful 1986 gubernatorial campaign of endorsed Bob Martinez (a Republican). His endorsement of Martinez came prior to the 1986 Republican gubernatorial primary, with Suarez actively campaigning for him.
After the police shooting of Clement Lloyd, a Black motorcyclist, Suarez personally engaged with a crowd of protesting residents. This gesture earned him praise. According to a March 30, 1993 article in The Miami Herald, "In 1989, [Suarez] won national admiration when he waded through hostile crowds in Overtown during civil disturbances to try to make peace."
Suarez received attention for refusing to greet South African President Nelson Mandela during his 1990 tour of the United States which included a stop in Miami. Suarez was in disagreement with Mandela's comments where he referred to Cuban President Fidel Castro as a "comrade in arms" due to Castro's support for the African National Congress. Suarez faced criticism for his refusal to greet Mandela, which led to a boycott by the local African American community of all Miami tourist and convention facilities until Mandela received an official greeting. Efforts to resolve the dispute failed for months, resulting in an estimated loss of over US$10 million in tourism revenue.
On October 7, 1990, Suarez issued a proclamation declaring "Yahweh ben Yahweh Day" in honor of the leader of the Nation of Yahweh, a religious sect based in Miami. A month later, the group's founder was indicted on charges of conspiracy to commit murder.
Suarez cited the construction of 1,500 affordable homes as one of his "proudest achievements" during his tenure. He was also given the name "pothole Mayor" for his attention to City neighborhoods. In 1993 Suarez got the Latin Builder's Association to donate $150,000 to rebuild the only Catholic elementary school in Overtown.
During his first tenure as mayor, some observers speculated that Suarez had a major future in politics ahead of him. In 1996, Florida International University political science professor Christopher Warren opined that Suarez, however, had failed to demonstrate a strong political drive during his first tenure, remarking, "Suarez never showed himself to be a particularly aggressive leader. He was never someone who had a strong agenda."
Having spent eight years as mayor, and perhaps grown momentarily bored with politics, Suarez opted against seeking re-election in 1993 in order to dedicate more time to his legal practice and his family.