"They knew everything," blared the weekly's report, first released online, as the publication stepped up coverage of a huge embezzlement scheme benefiting dozens of politicians, most of them members or allies of the ruling Workers Party (PT).
The print edition of the story will hit newsstands Saturday - just in time for Sunday's run-off poll.
Rousseff enjoyed an eight-percent advantage over Social Democrat Aecio Neves in the first round of voting on October 5 and the latest polls have her holding the advantage.
Rousseff blasted Veja's "criminal" allegations as "electoral terrorism," insisting there was no proof of any wrongdoing on her part.
"Today, this magazine has gone well beyond the limits of decency. It is a malevolent attempt to interfere in the result of the election in a dishonest manner," Rousseff said in a final campaign address.
"Brazilians will give their response to Veja magazine and its accomplices at the polls - and I shall give mine to the law," she said, indicating she plans to sue the publication.
Rousseff, 66, served as energy minister and later chief of staff under two-term (2003-2010) president Lula.
She also chaired the Petrobras board during part of the period when a former director of the company alleges the kickbacks scheme operated.
According to Veja, Alberto Yousseff, a shady money dealer who has testified to helping launder funds for the scheme, told police on Tuesday that "Planalto (the presidential palace) knew everything."
Asked by investigators exactly who knew everything in Planalto, Yousseff replied: "Lula and Dilma," Veja reported.
Neves for his part dubbed the allegations as "very serious," telling media that "Brazil needs a response from those governing the country" and slamming Rousseff's response as tantamount to attempted "censorship."
Rousseff has insisted throughout she knew nothing of the scheme, but conceded last week the ongoing investigation suggested wrongdoing was clearly afoot.
"If anything happened, and everything indicates that it did, I can guarantee all of the bleeding which may have existed has been stanched," Rousseff told Estado de S. Paulo daily.
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