Sectarian tension has been high in Iraq since the hanging of Saddam Hussein, the former Iraqi president, on Saturday.
The statement of the MCA, an umbrella grouping of Sunni religious leaders, did not identify the armed groups or say that they were Shia.
However, the suggestion in the statement that the fighters had links to government parties is a strong indication to Iraqis that it was accusing Shia groups.
After al-Maliki rushed through the hanging of Saddam, a Sunni, and a video was circulated showing the former Iraqi leader being taunted on the gallows by Shias, there have been fears of sectarian violence in the capital.
But there were no reports from Baghdad on Friday of anything out of the ordinary.
Hosni Mubarak, Egypt's president, has strongly condemned the conduct and timing of Saddam's execution at the start of a Muslim religious festival and questioned the legality of the sentence, passed by an Iraqi court while the country itself is under US control.
In an interview published on Friday in the Israeli daily Yediot Ahronot, Mubarak said that when it became clear that the hanging was imminent, he sent a message to George Bush, the US president, asking that it not be carried out during the Eid al-Adha holiday.
"[The execution] was disgraceful and very painful. I'm not going to say whether Saddam deserved the death penalty or not, I'm also not going to go into the question of whether that court is legal under the occupation"
Hosni Mubarak, Egyptian president
Mubarak said: "Don't do it at this time. Why is it necessary to hang [him] just at the time when people are saying the holiday prayers."
He said the insensitive timing was then followed by the clandestine video showing "shocking pictures, primitive pictures" of Saddam being taunted by his Iraqi guards and then dangling from a rope.
Mubarak said: "It was disgraceful and very painful. I'm not going to say whether Saddam deserved the death penalty or not, I'm also not going to go into the question of whether that court is legal under the occupation.
"When all's said and done, nobody will ever forget the circumstances and the manner in which Saddam was executed. They have made him into a martyr, while the problems within Iraq remain."
In a separate development, Ahmad Khatami, an influential Iranian cleric, has accused the United States of wanting to use Saddam's execution to stoke tensions between Shia and Sunni Muslims.
Khatami told worshippers at Friday prayers, in a sermon broadcast on state radio, that: "America's method is to start sectarian differences. They want to use Saddam's death to portray divisions among Shias and Sunnis.
"Do not doubt that the enemy's plan in Iraq and Iran is to inflame differences among Shias and Sunnis. In Iran and Iraq, for years, Shias and Sunnis have been living together peacefully."
Khatami is member of the Assembly of Experts, a clerical body, and a regular leader of Friday prayers in the capital, Tehran.
Saddam, who was executed on Saturday, was tried in a US-sponsored court but the US military said it had no role in the hanging and would have handled it differently.