The grisly finds were the latest in an endless stream of violence, much of it designed to destabilize Iraq's new government and hasten a US retreat.
More than 450 people have been killed in just over two weeks since Prime Minister Ibrahim al-Jaafari's Cabinet was announced. At least 10 more Iraqis were killed in a spree of bombings and shootings Sunday.
On a lightning visit, Secretary of State Condoleezza Rice urged Iraqis to be patient, saying the insurgency can be beaten with the help of a strong political alternative.
"The insurgency is very violent but you defeat insurgencies not just militarily," Rice said after meeting with al-Jaafari and other officials in Baghdad and the northern Kurdish region. "The Iraqis ... are now going to have to intensify their efforts to demonstrate that in fact the political process is the answer for the Iraqi people."
Police in Baghdad's Sadr City, a Shiite-dominated slum, discovered 13 slain men, most appearing to be in their 20s and three of them bearded, lying face down in a shallow grave in a lot Sunday. Residents told police a truck dumped the bodies there early Sunday and three people covered them with dirt, said policeman Lt. Col. Hafidh Maan.
An Associated Press photographer saw the bodies lying in the ground, their hands tied behind their back, eyes blindfolded and at least three bullet wounds in each of their heads. The men were wearing civilian clothes, and had no identifying documents.
Members of the Badr Brigades, a Shiite militia, discovered the bodies while searching for hidden homemade bombs, police said.
Eleven more bodies were found late Saturday at a deserted chicken farm in Huqoul, a town in the Latifiyah area, about 25 miles south of the capital, said police Capt. Muthna Khalid Ali.
The victims had their hands tied behind their backs and gunshot wounds to the head, according to another AP journalist at the scene.
Two trucks riddled with bullet holes stood nearby. Identity documents and keys found on two of the bodies identified them as the owners of the truck and among 11 truck drivers kidnapped in the area last month, Ali said.
The next day, the bullet-riddled bodies of a judge, an Education Ministry official and a bodyguard were discovered near the same farm and taken to nearby Iskandariyah General Hospital, an official there said.
A fourth body viewed at the hospital was found dumped on a major road, with a bullet wound in the head, he said. The official asked not to be named.
The bodies of 10 Iraqi soldiers were found Saturday in the battleground city of Ramadi, 70 miles west of Baghdad, an Interior Ministry statement said. The men were shot, but no further details were provided.
Iraq's Sunni Arab-driven insurgency regularly targets Iraqi security forces, government officials and others deemed to be collaborating with US-led forces in the country. Others are kidnapped and sometimes killed to extort lucrative ransoms from their families.
But there have also been a stream of retaliatory attacks between armed Sunni and Shiite groups. Recently, they have included deadly bombings seemingly targeting civilians from the Shiite majority who dominate Iraq's first democratically
A leading Shiite cleric, Sheik Qassim al-Gharawi, and his nephew were killed in a drive-by shooting in eastern Baghdad on Sunday, police said. Across town, gunmen in two cars shot and killed Industry Ministry official Col. Jassam Mohammed al-Lahibi and his driver.
Three more people, two of them carrying identification cards from local media outlets, were shot and killed in their car on the road to Latifiyah, said Saadun Mohsin, an official at nearby Mahmoudiyah General Hospital. Soldiers brought their bodies to the hospital, he said.
Two suicide attackers struck within five minutes in a busy downtown street in Baqouba, 35 miles northeast of Baghdad.
The first, a car bomber, targeted the provincial governor's convoy, police said. Gov. Raed Rashid Hamid al-Mullah Jawad escaped unharmed, but three of his guards were injured.
Minutes later, a suicide bomber dressed as a police lieutenant blew himself up at a court building just 500 yards away, killing four policemen, said police Brig. Gen. Adil Mollan. Hospital officials said 37 people were injured in the two attacks.
About 20 minutes later, at least seven mortar rounds slammed into a residential neighborhood of the city, badly damaging five homes and injuring three men and one woman, police said.
On Monday, a roadside bomb targeting an Iraqi army convoy in southwest Baghdad killed two civilians. Four people were wounded, said police Lt. Hussein Alwan.
Rice acknowledged the security problems Sunday, but said Iraq's new government realizes it must move quickly to write a constitution that reflects the full spectrum of ethnic and religious groups in Iraq and hold fresh elections by year's end.
Al-Jaafari confirmed his commitment to increasing the participation of Iraq's disaffected Sunni Arab minority in the new political dispensation.
"We assert that our new political system is a system that respects people's faiths and respects pluralism," al-Jaafari told reporters.
"It is a regime that respects the rights of citizens and respects their role in the new institutions."
Sunnis dominated under Saddam Hussein's brutal regime, but most stayed away from landmark parliamentary elections in January and they are underrepresented in al-Jaafari's government.
It was Rice's first trip to Iraq as the top U.S. diplomat. When Rice was President Bush's national security adviser, she was a chief architect of the war in Iraq.
In other developments:
Australia's top Islamic leader said kidnappers holding the Australian engineer Douglas Wood hostage have indefinitely extended their deadline for the country's forces to start withdrawing from Iraq. The Australian government has refused to meet the demand. Sheik Taj El Din al-Hilaly flew to Baghdad last week to try to negotiate the release of Wood, a California resident captured more than a week ago.
The Sunni militant Ansar al-Sunnah Army released a video it said shows the aftermath of the ambush that led to the capture of a Japanese security contractor.
The video, which appeared on an Islamic Web site, did not give any indication of Akihito Saito's fate but purportedly showed the killing of four foreign contractors and 12 bodyguards.
A Japanese Foreign Ministry spokesman said it was believed to be genuine.
(Associated Press writers Bushra Juhi in Baghdad and Ali Fatlawi in Latifiyah contributed to this report.)