The group -- the Mujahedeen Shura Council -- said it had beheaded three of the men and shot one to death.
A video also posted on the Web site appeared to show one of the men being beheaded, another man already beheaded and a third man being shot in the head. The fourth man did not appear in the video.
Russian officials were trying to verify the development.
The same group posted a statement last Monday demanding Moscow withdraw its troops from Chechnya and "release all our brothers and sisters" from prison within 48 hours.
In the statement last week, the group added, "God enabled the lions of unification to capture four Russian diplomats in Iraq and kill a fifth," alluding to an attack June 3, when a car belonging to the Russian Embassy in Iraq came under fire.
Embassy official Vitaly Titov was killed in the attack, and diplomats Fyodor Zaitsev, Rinat Agliuglin, Anatoly Smirnov and Oleg Fedoseyev were kidnapped.
The claims could not be verified, but the Web site has been used by insurgent groups in the past to post messages.
The disclosure of the Russian diplomats' deaths -- and deadly violence across the country -- unfolded on an important day for the Iraqi government.
Prime Minister Nuri al-Maliki on Sunday announced his national reconciliation plan, which extended an olive branch to some Iraqi militants and granted the phased release of 2,500 detainees from Iraqi prisons. Those releases already have begun.
Al-Maliki's plan is aimed at placating militant Sunni factions and countering sectarian strife in the country, as well as outlining the steps for Iraqis to assume control of the volatile security situation.
"We need to drum up support to face the criminals and the terrorists to reactivate our economy by creating jobs, and giving opportunities and providing services to the people so to show everyone that we are serious in our commitment to serve our nation," al-Maliki said.
The prime minister's plan, which he presented to parliament, stipulates amnesty will be granted to detainees who "have not committed war crimes, crimes against humanity, crimes against Iraqis and acts of violence."
U.S. senators called al-Maliki's plan a positive step but expressed concerns about its amnesty provision.
Insurgents on Sunday cranked up their assaults throughout Iraq, killing at least 32 people in scattered attacks, mostly in Diyala province, and kidnapping 16 others in a brazen abduction in Taji.
Gunmen killed 23 people on Sunday in nine separate incidents in Diyala, an official with the provincial police Joint Coordination Center told CNN.
In Baquba, the provincial capital, gunmen sped through the streets and opened fire, killing three people -- including a high-ranking police officer -- in three separate shootings between 10:30 and 11:30 a.m., a Baquba police official said.
Gunmen also shot and killed four oil-tanker drivers on a highway nearly 50 miles (80 kilometers) east of Baquba in Mandali, near the Iranian border.
In Muqdadiya, about 24 miles north of Baquba, three people were killed and another wounded when gunmen attacked a civilian car about 1:30 p.m.
Minutes later in the same town, a drive-by shooting resulted in the death of an Iraqi police officer and wounded three other bystanders. Gunmen in Muqdadiya also killed three Iraqi police about 3:30 p.m.
Insurgents armed with machine guns and rocket-propelled grenades gunned down soldiers at an Iraqi army checkpoint, killing six and wounding four others, at 3 p.m. in Khan Bani Saad, about 12 miles south of Baquba.
Three more Iraqi police officers were killed around 4 p.m. near a bus station in central Baquba after gunmen opened fire at them in a drive-by shooting.
In Baghdad, two people were killed and five wounded when a bomb exploded in a minibus around noon, emergency police officials said.
Four passers-by at the Shorja market in central Baghdad were killed and 23 wounded when a bomb ripped through the area around 11:30 a.m., a Baghdad emergency police official said.
An hour earlier in eastern Baghdad, a car bomb detonated at a police checkpoint, killing one police commando and wounding three others, a Baghdad emergency police official said.
In the northern city of Mosul, two guards were killed and four others injured when a truck bomb exploded outside the Supreme Council for the Islamic Revolution in Iraq, a top Shiite political movement.
The U.S. military announced Sunday it has charged two soldiers in the death of an unarmed Iraqi in February in Ramadi.
The two soldiers, Spec. Nathan B. Lynn and Sgt. Milton Ortiz, Jr., are members of the Pennsylvania National Guard's 1st Battalion, 109th Infantry (Mechanized).
According to the military, Lynn was charged with one count of voluntary manslaughter for allegedly shooting the man on February 15 in front of a home near Ramadi.
Lynn and Ortiz each face one count of obstructing justice. They are accused of conspiring with another soldier who allegedly placed an AK-47 assault rifle near the wounded Iraqi man.
That soldier was redeployed and demobilized before criminal proceedings were initiated.
Word of the charges against Lynn and Ortiz comes just days after seven Marines and a Navy corpsman were charged with killing a civilian in Hamdaniya, in April. (Full story (http://edition.cnn.com/2006/US/06/21/hamdaniya/index.html))
Separately, four soldiers from the 101st Airborne Division were charged last week in connection with the shooting deaths of three detainees in Salaheddin province in May, the military said. (Full story (http://edition.cnn.com/2006/WORLD/meast/06/21/salaheddin/))