"There was an understanding with the Americans, as paradoxical as it may seem," Primakov told the Russian daily Gazeta in a lengthy interview.
"Why weren't the bridges of the Tigris blown up when the American tanks approached Baghdad? Why weren't Iraqi aviation and tanks used, and where are they now?" asked Primakov, a former head of the Russian secret service and a specialist in Arab affairs who was formerly on good terms with Saddam.
"Why was there an immediate ceasefire? Why was there practically no resistance a year ago?" he added.
Primakov, who now heads Russia's chamber of trade and industry, also cast doubt on the authenticity of footage of Saddam's reported capture that circled the world on December 14.
"They showed two soldiers with guns with palm trees in the background near the hole (where Saddam was reportedly hiding). At that time of year, date palms are never in bloom," he said.
"Finally, any man can tell you that such a long beard (as Saddam had when he was reportedly caught) could not grow in seven months," he said.
"All evidence suggests that Saddam surrendered earlier and the story of the hole was invented later," he said.
Primakov, who was also Russian foreign minister, made two secret trips to Iraq at the request of President Vladimir Putin, shortly before the invasion by US and British troops.
During the 1970s and 1980s Primakov was one of the most important Arab world hands in the KGB, and later was instrumental in securing oil deals for Russian companies in Iraq. According to reports in the Saudi press and some Arab television stations during the Iraq war, he had also taken part in a deal taking Saddam Hussein out of Baghdad in a Russian diplomatic convoy that was meant to be carrying Russian diplomats. At the time these reports suggested that Saddam had abandoned Iraq for Russia or one of the former Soviet republics in exchange for not putting up resistance to the US invasion.