(CNN) -- Five Republican presidential candidates are boycotting a proposed Univision debate because of what they say were unethical reporting practices by the Spanish-language network in how it handled a story concerning Republican Sen. Marco Rubio of Florida.
Univision Tuesday denied allegations that it told Rubio it might not broadcast a story about his brother-in-law's 24-year-old drug conviction if the freshman senator appeared on "Al Punto," one of the network's news programs. Univision has called the allegations "absurd" and says its July story of the drug bust was reported fairly and accurately.
"With respect to Sen. Rubio, Univision covered the issue in the same objective and impartial manner in which we cover all important news," Isaac Lee, president of Univision news, said in a written statement. "Univision did not offer to soften or ignore the report about an anti-drug raid that involved the family of Sen. Rubio. We would never make such an offer with any protagonist in a news report and we did not make an offer in this case."
Rubio, the former Florida House speaker, is a freshman senator and a star among Republicans, who talk about him as a possible running mate on the GOP ticket next year.
Univision has tried for quite some time to have him as a guest on its network news programs, where he would likely face tough questions about his stance on immigration reform.
The Miami Herald was the first news organization to report the story. It said it obtained its information from various sources, including some from within Univision.
A spokesman from Rubio's office said that "The Miami Herald's article is accurate. Univision employees themselves were the first to come forward with this account, and we confirmed it."
Rep. David Rivera, a close friend of Rubio, told CNN Wednesday that he had talked with Rubio and his family members "minute by minute as the incident was occurring."
"I don't think the staffers of Marco Rubio's office were ... inventing those details. They were very, very clear details. ... It was a clear exchange of having the exclusive interview with the senator and that way, not airing the report about the relative of Marco Rubio," the Republican congressman said.
The allegations against Univision prompted three Hispanic GOP leaders in Florida to call for the GOP presidential candidates to boycott Univision's proposed debate in late January in the Sunshine state, just before Florida holds its presidential primary.
The candidates who have agreed to boycott the debate are former Massachusetts Gov. Mitt Romney, Texas Gov. Rick Perry, former Utah Gov. Jon Huntsman, businessman and former Godfather's Pizza CEO Herman Cain, and Rep. Michele Bachmann of Minnesota.
Univision was proposing to hold a debate on January 29, two days before Florida Republicans' presidential primary. CNN and the Republican Party of Florida are hosting a presidential debate in the days before the primary, and NBC and Telemundo, another Spanish-language network, also are planning to host on a debate in Florida around the same time.
CNN's Ione Molinares, Paul Steinhauser and Robert Lenz contributed to this report.