Iraqi officers found the bodies of at least 17 murder victims lying around the capital in the previous 24 hours, a US spokeswoman said, as sectarian death squads pursued their relentless campaign.
The soldier, an American of Iraqi descent working as a translator, went missing at 7.30pm (1630) GMT) on Monday at a time when most Iraqis were heading home to celebrate the feast of Eid-ul-Fitr with their families.
"We are searching in various locations for him based on intelligence and leads we get," a US military spokeswoman told AFP. There are some 15,000 American US troops in Baghdad attached to a joint US-Iraq operation to quell a brutal sectarian conflict, and their casualties are mounting, with this month on course to be the bloodiest in two years.
The soldier has been listed as "duty status-whereabouts unknown", which implies the military does not know whether he chose to go absent without leave or was the victim of an attack or an abduction.
"Coalition and Iraqi Security Forces immediately responded to attempt to locate the soldier, the search is ongoing," a US statement said.
Akbar al-Saedi, an MP from the Supreme Council for the Islamic Revolution in Iraq (SCIRI), said the offices of the party's Al-Forat television network were searched overnight by US soldiers.
"They remained there for about four hours until the Iraqi national security adviser, Mowaffaq al-Rubaie, came to talk to them and explain the duties of our people," he told AFP.
As well as searching the station, the troops fanned out to neighbouring houses in the Karrada district of central Baghdad, he said. They seized some unlicensed weapons, but did not appear to find what they were looking for.
The Shia party SCIRI is the most powerful single bloc in Prime Minister Nuri al-Maliki's coalition. It was founded with Iranian help during the Iran-Iraq war of the 1980s, but denies being controlled by Tehran.
The holy month of Ramazan, which came to an end with this week's three-day Eid-ul-Fitr feast, has been marked by a spectacular rise in attacks on both Iraqi civilians and US forces.
At least 12 American soldiers were killed over the weekend, most of them in Baghdad and, with 87 dead in the first three weeks of October, this month is on course to be the bloodiest for US forces since November 2004.
Meanwhile, gun and bomb attacks on civilians have increased by more than 20 percent, forcing Iraq's bitterly divided communities of Kurds, Sunni Arabs and Shia Arabs further apart and increasing the risk of all-out civil war.
For SCIRI, the answer is to divide Iraq into autonomous federal regions with only loose central control, and the party's powerful leader Abdel Aziz al-Hakim used his set-piece Eid speech to push this agenda.
"Federalism will guarantee that the injustice of the past will not revisit our children nor our grandchildren," the bearded leader told an audience of hundreds of followers in Baghdad.
Hakim and his supporters argue that in order to prevent a resurgence of Sunni dominance of Iraq, such as that which prevailed under Saddam Hussein's ousted regime, the Shias of south and central Iraq must have self-rule.
On Tuesday he accused opponents of federalism of wanting "to bring back dictatorship and unjust central power," while insisting that SCIRI did not want to destroy or partition Iraq but to strengthen it.
Hakim's Sunni opponents and many Shias, including cleric Moqtada al-Sadr, fear SCIRI's vision of an eight province autonomous Shia zone would put the Iranian-backed party in command of Iraq's oil wealth.
Some in Washington also fear that federalism could accelerate the break-up of Iraq and increase the violence gripping the country.
Nevertheless, the US and British governments are under pressure from their electorates and oppositions to find a new strategy to halt the fighting and bring home the 142,000 American and 7,200 troops in Iraq.
This week the White House confirmed it had asked Maliki's government to meet certain "benchmarks and milestones" in combating the violence, disarming illegal militias and working out a fair formula to share oil revenues.

Copyright AFP (Agence France-Presse), 2006