The Heinz endowments, two foundations worth more than $1 billion, said the money went to two projects in Pennsylvania instead, The Miami Herald reported Wednesday.
The endowments come from the fortune of Teresa Heinz-Kerry, wife of the Democratic nominee for president.
They said $8 million went from the endowments to the Tides Foundation and Center and was eventually used by the Cubans for the Internet. The Tides Foundation said the accusations were false.
The accusations and denials were delivered in dueling news conferences Tuesday.
In a separate statement, Hialeah, Fla., Mayor Raul Martinez, a Kerry supporter denounced the accusation.
"This is incredible that the Bush campaign has stooped so low and talked these three Cuban congressional members into telling straight out lies," Martinez said.