MIAMI – The Univision television network denied allegations Tuesday that it told Republican Sen. Marco Rubio it might not broadcast a story about a relative’s decades-old drug conviction if he appeared on its news programs.

The story about his brother-in-law’s late 1980s cocaine trafficking conviction ran in July and Rubio did not appear on the network. The Spanish-language network says it never used the story to pressure Rubio to appear. Rubio’s spokesman declined comment to The Associated Press but told The Miami Herald that the network’s head of news insinuated the offer on a conference call. That description of the call matched a similar account that the newspaper obtained from separate sources.

The allegations prompted three Hispanic Republican leaders to call for Republican presidential candidates to boycott Univision’s efforts to plan a debate in January. Mitt Romney, Rick Perry and Jon Huntsman said Tuesday they would boycott.

Univision has long sought Rubio as a guest on its network news programs, where he would likely face tough questions from top anchors Jorge Ramos and Maria Elena Salinas about his conservative stance on immigration reform. Univision denies it ever tried to use the story to pressure Rubio into appearing.

Univision heavily promoted its July 11 story on the late 1980s conviction of Orlando Cicilia, the husband of Rubio’s sister, during the federal-led “Operation Cobra.” Marco Rubio was 16 at the time and had nothing to do with the case. Cicilia was given early release in 2000. The in-depth story was widely ignored by English-language media because of a lack of relevance to the senator’s political career.

The Herald first reported Saturday allegations that on a July conference call with Rubio staff, Univision president of news Isaac Lee insinuated the network would tone down or pull the story if Rubio appeared on one of its news programs. The Herald story cited unnamed Univision sources, as well as notes from Rubio’s staff members who it said matched the reported account.

Rubio officials told the AP on Tuesday that they did speak to the Herald about the allegations until after the Univision sources came forward and they have decided not to make further statements about the story.

Univision said in a statement that several participants were on the call with Rubio’s office for an “off-the-record discussion” about the cocaine story, including two of its top lawyers. The company said it has not announced any planned debate or reached out to any candidates.