Iraqi police discovered a body floating in the Euphrates River south of Baghdad Wednesday that is believed to that that of a missing U.S. soldier.

According to a U.S. military official, a second body was found in the area near where the first body was discovered. The official, who requested anonymity because the information has not yet been released, said there was no indication yet whether the body was another of the three missing soldiers.

Maj. Gen. William Caldwell, chief U.S. military spokesman in Iraq, told reporters that U.S. authorities took custody of the body but have not determined if it was that of one of three soldiers missing since May 12.

"Iraqi police did find the body of a man whom they believe may be one of our missing soldiers," Caldwell said. "We have received the body and we will work diligently to determine if he is in fact one of our missing soldiers."

A U.S. military source told FOX News: "We do believe there is a strong possibility it is one of our soldiers."

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If the body proves to be one of the missing soldiers, his family will be notified first, Caldwell said.

The discovery of the body in Musayyib, about 40 miles south of Baghdad in Babil Province, came as U.S. troops and Iraqi forces continued their massive search for the three soldiers abducted May 12 in an ambush on their patrol near Mahmoudiya, about 20 miles south of Baghdad.

The man had been shot in the head and chest, Babil police Capt. Muthana Khalid said.

Iraqi police using civilian boats searched for other bodies on the river in Musayyib, about 40 miles south of Baghdad, and U.S. troops intensified their presence on a nearby bridge as helicopters flew overhead, witnesses said.

Hassan al Jibouri, 32, said he saw the body clothed in a U.S. military uniform with head wounds and whip marks on its back floating on the river Wednesday morning. He and others then alerted police.

Later Wednesday, police in Babil province reported they had discovered two more bodies in the river and suspected they belonged to the other two soldiers.

Caldwell only confirmed the discovery of one body.

In an interview with the Army Times newspaper last week, Gen. David Petraeus, the top U.S. commander in Iraq, said he believed at least two of the missing soldiers were alive.

"As of this morning, we thought there were at least two that were probably still alive," he said in the interview, which was posted on the newspaper's Web site on Saturday. "At one point in time there was a sense that one of them might have died, but again we just don't know."

The military has warned that U.S. casualties were likely to increase as troops made more frequent patrols during the U.S.-led security crackdown in Baghdad, now in its fourth month.

The captured soldiers are Pfc. Joseph J. Anzack Jr., 20, of Torrance, Calif.; Spc. Alex R. Jimenez, 25, of Lawrence, Mass.; and Pvt. Byron W. Fouty, 19, of Waterford, Mich.

Iraqi Prime Minister Nouri al-Maliki, meanwhile, announced he was ready to fill six Cabinet seats vacated by politicians loyal to radical anti-American Shiite cleric Muqtada al-Sadr in a mass resignation last month.

Al-Sadr, who went into hiding in Iran at the start of the Baghdad security crackdown, ordered his ministers to quit the government over al-Maliki's refusal to call for a timetable for U.S. withdrawal.

The deaths of the seven soldiers and two Marines in a series of attacks Monday and Tuesday brought the American death toll for the month to at least 80. Last month, 104 U.S. troops were killed in Iraq.

One of Wednesday's suicide bombings hit a cafe in the town of Mandali, on the Iranian border 60 miles east of Baghdad. The attacker walked into the packed cafe and blew himself up, killing 22 people and wounding 13, police said.

The cafe in the mixed Sunni, Shiite and Kurdish city was popular with police officers — but none was there at the time, police said. A man in his 30s wearing a heavy jacket despite the heat was seen walking into the cafe seconds before the blast, according to police.

In the second suicide assault, a bomber blew himself up in the house of two brothers who were supporting a Sunni alliance opposed to Al Qaeda in Anbar province, killing 10 people, including the men, their wives and children, police Lt. Col. Jabar Rasheed Nayef said.

The attacker, a 17-year-old neighbor, broke into the house of the two men, Sheik Mohammed Ali and police Lt. Col. Abed Ali, and detonated his bomb belt late Tuesday in Albo Obaid, about 60 miles west of Baghdad.

The targeted men were part of the Anbar Salvation Council, a group of Sunni tribal leaders backing the government's fight against Al Qaeda.

In Washington, National Security Council spokesman Gordon Johndroe said U.S. and Iraqi officials were planning to increase again the number of Iraqi security forces to help quell violence in the country.

The review was undertaken as President Bush's new military-political team in Iraq — Petraeus and U.S. Ambassador Ryan Crocker — assessed strategy for the four-year-old war.

"Gen. Petraeus and Ambassador Crocker have been working on the specific tactics" needed for the strategy President Bush announced in January — a troop buildup to calm Baghdad so Iraqis can make political and economic progress, Johndroe said.

About 337,000 Iraqi police and soldiers had been trained and equipped as of May 9, according to Defense Department statistics. Officials hope to have the currently planned 365,000 in place by the end of the year, Brig. Gen. Michael Jones, deputy director for political-military affairs in the Middle East for the Joint Chiefs of Staff, told lawmakers Tuesday.

Complete coverage is available in FOXNews.com's Iraq Center.

The Associated Press contributed to this report.