Five Iraqi sports officials have been released in Baghdad, but gunmen are still holding the country's Olympic Committee chief and many others.
They have not said who carried out the abductions or why.
Olympic chief Ahmed al-Hadjiya and 30 others were taken after being stopped by uniformed men on Saturday.
Police said the incident took place at a conference centre near central Baghdad, and that the kidnappers wore Iraqi army or police uniforms.
The officials were on their way to the conference in Baghdad's Sadoun district in a fleet of as many as 20 cars when they were stopped by the uniformed men.
Among those freed on Sunday was Nashat Maher, an adviser to the Iraqi Olympic Committee.
"He was found lying by the side of the road, blindfolded, in an eastern district of the capital," IOC official Mohammed al-Habash told AFP news agency.
A driver and three other guards were also released, he added.
Kidnappings are very common in Baghdad, mostly carried out for ransom.
Prior to the US-led invasion of Iraq in 2003, Iraq's Olympic committee was led by former President Saddam Hussein's son Uday.