Another security official put the figure at 25 and said a brigadier general in the traffic police was the highest-ranking figure. Most are low-level ministry employees, he said.
The official, who has access to the investigative file, spoke on condition of anonymity because he was not authorized to speak about the matter to the media.
A third security official said those in custody were believed to have links to al-Awad, or "Return," a Sunni underground organization founded in 2003 to try to restore Saddam and the Baath party to power.
He also spoke on condition of anonymity because he was not supposed to release the information.
But Khalaf denied that the group had links to al-Awad.
The U.S. military referred all inquiries to the Iraqi government.
Iraq's 2005 constitution bans the Baath party and any group that uses its symbols and ideology "regardless of the name that it adopts."
Some Iraqi politicians also expressed doubt that the plotters were actively trying to overthrow the government.
"I think talking about a coup is an exaggeration," Abbas al-Bayati, a senior lawmaker of the Supreme Iraqi Islamic Council, the largest Shiite party, told Al-Arabiya television.
He described those arrested as "a semi-organized group" but said the fact that they were trying to restore the Baath party pointed to shortcomings in Iraqi security in Baghdad and elsewhere.
Hadi al-Amiri, the head of the Iraqi parliament's security committee, told Associated Press Television news that "reports speaking about a coup attempt are baseless. In fact, coups are usually carried out by the army and not by police."
Mahmoud Othman, a senior Kurdish bloc lawmaker, said he hoped "the move against those arrested is not politically motivated or aims at electoral gains".
The ministry's director of internal affairs, Gen. Ahmed Abu Raqeef, denied a report in The New York Times that he was among those arrested.
"I am still in the ministry, carrying out my duties, and these accusations are baseless," Abu Raqeef said at a news conference.
The Baath Party ruled Iraq for 35 years until Saddam's regime was ousted by a U.S.-led invasion in 2003. The party was founded in Damascus, Syria, in the 1940s as a secular, socialist Arab nationalist movement. It later split along national lines and still rules in Syria.
Outlawing the Baath party was the first official act of the U.S.-run occupation authority which ruled until June 2004. The purge of thousands of Baath party members from government jobs cost the country the services of skilled people who knew how to run ministries, university departments and state companies.
In February, Iraq's presidency council issued a new law that allowed lower-ranking former Baath party members to reclaim government jobs.
The measure was thought to affect about 38,000 members of Saddam's political apparatus, giving them a chance to go back to government jobs. It would also allow those who have reached retirement age to claim government pensions.
Also Thursday, the speaker of the Iraqi parliament, Mahmoud al-Mashhadani, returned to the chamber a day after saying he was resigning.
Al-Mashhadani claimed he was resigning Wednesday during a shouting match over the jailing of the Iraqi journalist who became a folk hero after throwing his shoes at President George W. Bush during a Sunday news conference with Prime Minister Nouri al-Maliki.
It was unclear at the time whether al-Mashhadani, who has a history of erratic behavior, spoke out of pique or intended the statement as a formal announcement.
"Regardless of his announcement resignation he has come today in session," said Salim Abdullah, spokesman for the largest Sunni bloc in parliament. Al-Mashhadani also is a Sunni.
The journalist, Muntadhar al-Zeidi, remained in custody on Thursday.