The allegation from the Iraqi Islamic Party came as the prime minister, Nouri al-Maliki, tried to end speculation of a power struggle in his ruling Shia alliance on Tuesday by announcing the release of 2,500 prisoners.
On Monday armed assailants wearing police uniforms attacked bus stations in central Baghdad, grabbing people, including travellers, merchants and vendors selling tea and sandwiches.
The Sunni group said it was certain that Iraqi police carried out the abductions, although it did not provide specific evidence.
"The Iraqi police denied their involvement in this operation, despite the fact that it occurred in broad daylight ... and in central Baghdad," party member Alaa Maki said at a news conference.
Adnan al-Dulaimi, a Sunni politician, appealed for the government and US-led forces to take action against such attacks and urged the appointment of interior and defence ministers as soon as possible.
"The killing operations have become a phenomenon," he told reporters. "Fifty Iraqis have been abducted and the Iraqi officials have done nothing to stop those behind these terrorist acts.
"I call on the political blocs to expedite the appointments of the interior and defense ministers. It might reassure the Iraqi people and end these barbaric acts."
The Shia-dominated interior ministry oversees the police and has previously been accused of backing militias perpetrating sectarian violence.
It denies that its forces were behind the kidnappings on Monday and has announced an internal inquiry into the incident.
The Iraqi Islamic Party accuses
the police of staging a cover-up
A statement from the ministry said: "The police chief of Salhiya, the head of the emergency police and the traffic police have all been questioned in the investigation into the incident."
Preventive measures will also be taken to ensure such an incident does not happen again, the statement continued, saying anyone suspected in this case will be arrested.
Meanwhile, al-Maliki said the release of 2,500 prisoners would free those who had no clear evidence against them or had been mistakenly detained.
Five-hundred people will initially be released on Wednesday, he said, but did not give details.
Many current prisoners are from the once-dominant Sunni community. Al-Maliki said the prisoners would be released from US-run detention centres and Iraqi custody.
A UN human rights report last month said that there were 28,700 detainees in Iraq, including 5,000 held by the interior ministry.
The announcement comes amid comments from anonymous political sources that al-Maliki's rivals in the Shia Alliance have blocked his efforts to name interior and defence ministers and do not believe that his government will last.