"I would very much urge the leadership of Congress to call people back for a special session and get a bill passed," she said.
The clinic stop was Clinton's final campaign appearance in two days in vote-rich Florida that included fundraising parties in Miami. Immediately afterward, Clinton made an unannounced stop at a campaign office for Rep. Debbie Wasserman Schultz, the ousted Democratic National Committee chair, who faces a challenger in the state's Democratic primary on Aug. 30. Clinton's rival for the Democratic nomination, Sen. Bernie Sanders (Vt.), has endorsed Wasserman Schultz's challenger, Tim Canova, and is raising money for him.
"I want to have her in the Congress by my side working day after day," Clinton told staff and volunteers.
Wasserman Schultz was a Clinton ally, but the Clinton campaign was instrumental in forcing her to step aside last month following the publication of hacked emails showing DNC staff appearing to work against Sanders.
Wasserman Schultz showed no hard feelings Tuesday and pledged to "help carry the state of Florida and will carry you on the shoulders of Florida voters all the way to the White House.”
"We have to make sure that Donald Trump never gets anywhere near the White House," she told Clinton. "This man is dangerous. He doesn’t have the temperament. He’s engaged in misogynistic, horrific, bigoted criticism and language that is absolutely unacceptable for anyone but particularly for someone who is the nominee of one of our major political parties."
Separately, the Clinton campaign said it was unaware that Seddique Mateen, the father of the suspect in the June mass shooting at an Orlando nightclub, secured a prime seat at a Clinton rally on Monday in Kissimmee, near Orlando. Mateen told Florida television station WPTV that he had been "invited by the Democratic Party."
Late Tuesday, following extensive news coverage of the elder Mateen's presence, Clinton spokesman Nick Merrill issued an additional statement.
"She disagrees with his views and disavows his support," Merrill said, apparently in reference to reported anti-gay remarks made by the elder Mateen.
Zika poses a danger of severe birth defects. At the clinic, Clinton said the United States has an opportunity to contain the outbreak now, Clinton said.
"This is really the canary in the mine," she said.
Clinton’s call follows those of Democratic leaders in Congress but is timed to apply extra pressure on Republicans now that the virus has spread inside the United States.
For Clinton, focusing on Zika and the public health risk to women and babies in South Florida fits into political efforts to turn out Latino and urban voters here and to highlight her biography as an advocate for women and children.
By coming to the "hot zone" where Zika has been transmitted locally, Clinton was highlighting that Trump has not visited the area.
The Borinquen Medical Center is inside a zone of the city that the Centers for Disease Control and Prevention has advised pregnant women against visiting. It is close to the trendy Wynwood arts and restaurant neighborhood, where 17 cases of Zika infection were diagnosed. The clinic is offering free Zika testing and is working to spread information about prevention of new cases.
"I disagree with those who say that Zika is an insignificant issue. My opponent in this race — his campaign officials have said that," she said. "That does a great disservice."
The Republican National Committee accused Clinton of "playing politics" with the health crisis.
“If Hillary Clinton was really concerned about Zika, she’d be telling her running mate, Tim Kaine, to stop blocking funding in the Senate instead of holding a photo op," RNC spokesman Michael Short said.
That was a reference to Democrats' rejection of Republican funding proposals that they said came attached with politically motivated strings, including about funding for Planned Parenthood.
Kaine (Va.) has said that he would return to Washington for a debate and vote on Zika funding.
Republicans and Democrats in Congress have been deadlocked for months over the fate of a $1.1 billion spending bill that would help fight the spread of Zika. Negotiations over a bipartisan spending package crumbled in late June, with leaders of both parties unwilling to reopen talks. Congress is out of session for August, and lawmakers are not expected to resume legislative business until after Labor Day.
Senate Minority Leader Harry M. Reid (D-Nev.) has urged Senate Majority Leader Mitch McConnell (R-Ky.) to call a special session.
“Zika is a public health emergency that requires immediate bipartisan action, and the American people can’t afford to wait several weeks for a response,” Reid said earlier this month.
This month, Sen. Marco Rubio (R-Fla.) joined Democrats in calling for Congress to return to vote on a Zika bill. Sen. Charles E. Schumer (D-N.Y.) said in an interview with Politico on Tuesday that the congressional delay may hurt Rubio in his contested reelection bid.
Miami-Dade Mayor Carlos A. Giménez, a Republican who previously endorsed Jeb Bush and Rubio for president, was on hand for Clinton's visit but did not speak or endorse her.
The CDC announced the Zika outbreak in Miami early this month. The unprecedented domestic travel warning covers pregnant women and their partners. It applies to a one-square-mile area north of downtown Miami, with borders drawn by the CDC.
Additional cases are likely to be identified as testing continues, which could mean an expansion of the travel advisory.
Zika’s first mosquito-borne transmission in the United States has not sparked alarm among the vast majority of Americans, who do not fear infection, according to a new Washington Post-ABC News poll.
Sixty-five percent of Americans say they are “not too” or “not at all” worried about being infected with Zika or about having an immediate family member become infected, a figure that has hardly changed from 67 percent in June.
Scott Clement, Brady Dennis, Emily Guskin, Drew Harwell and Lena Sun in Washington contributed to this report.