BAGHDAD, Nov. 2 — The top American military spokesman here on Thursday played down recent discord between the American and Iraqi governments, saying that while there had been “disconnects,” the leaders of both countries were working closely to achieve political stability in  Iraq.

“A transition is not always a pleasant thing to watch as it happens,” the spokesman, Maj. Gen. William B. Caldwell IV, said during a news briefing in Baghdad. “We need to have more dialogue, as was clearly evidenced by the fact that there have been some disconnects that have occurred in this transition period.”

On Tuesday, in the latest public flare-up of tension, Prime Minister Nuri Kamal al-Maliki, under pressure from Shiite political leaders and outraged Baghdad residents, demanded that American troops remove a week-old cordon that had been set up around the Shiite district of Sadr City as part of the search for a missing American soldier.

General Caldwell said Thursday that a “tremendous amount of political activity” was under way to secure the release of the soldier, who was reported taken on Oct. 23 after he left the fortified Green Zone, without permission, to visit relatives in central Baghdad.

“There is ongoing dialogue that is being done at different levels at this time,” the general said, though he refused to provide any details of those conversations.

General Caldwell confirmed that the soldier was Specialist Ahmed Qusai al-Taie, a 41-year-old Iraqi-American reservist, and that he was married to an Iraqi woman. His wife was among the relatives Specialist Taie was visiting when he was abducted, the general said, adding that officials believed that the soldier was still alive and being held by his original captors.

Mahmoud Raouf Mahmoud/Reuters - A bomb exploded in a crowded market in the New Baghdad neighborhood Thursday, killing one and wounding 22, a government official said.

The American command has dedicated more than 2,000 American troops and more than 1,000 members of Iraqi security forces to the search operation, which has focused on Sadr City and the central Baghdad neighborhood of Karrada, where Specialist Taie was taken. The authorities suspect involvement by the Mahdi Army, a large Shiite militia that controls Sadr City and is loyal to the Shiite cleric

Moktada al-Sadr. The manhunt has angered some American troops in Iraq, who have privately complained that the military should not expend any additional resources, or put any troops at further risk, to search for a soldier who had violated military rules and exposed himself to danger by leaving his post without military protection. But on Thursday, perhaps addressing those complaints, General Caldwell said, “We never stop looking for our service members.” Prime Minister Maliki’s demand to end the search cordon put additional strain on an increasingly fractious relationship between him and President Bush. The Iraqi leader has wrestled for more independence from his American protectors, including greater control of Iraq’s security, which is dominated by the Americans. According to General Caldwell, the prime minister announced an initiative this week to expand the Iraqi military by about 18,700 troops. The top American military commander in Iraq, Gen. George W. Casey Jr., said last week that Iraqi security forces still needed 12 to 18 months before they would be ready to take full control of the country’s security.

But Iraq’s president, Jalal Talabani, offered a more conservative prediction, saying during a speech in Paris on Thursday that Iraq’s security forces would be ready to assume full responsibility in two to three years. “Two to three years are needed to build our security forces and say goodbye to our friends,” said Mr. Talabani, who is on a six-day visit to France. General Caldwell said some measurements of violence in Iraq had indicated a decrease since the holy month of Ramadan ended early last week, including a 23 percent drop in casualties across the country from the week before.

“Those statistics are promising, but as I’ve said before, one week does not constitute a trend,” he cautioned. Indeed, a wide range of attacks on Thursday drew from the entire repertoire of tactics used by the country’s death squads and criminal groups: vehicle bombs, mortar bomb attacks, bombs concealed along urban and rural roadways, ambushes, assassinations, drive-by shootings and kidnappings.

At least 37 people were killed, including civilians and security forces, and 97 wounded in more than two dozen incidents reported by the authorities in Baghdad, Baquba and Kirkuk, three of the country’s largest cities.

In Baghdad at least five people were killed and 53 were wounded when a bomb hidden on a motorcycle exploded in a crowded marketplace in Sadr City.

Separately, attackers shot and killed the dean of Baghdad University’s economics and management college, his wife and their son at the college’s front gate, an Interior Ministry official said.

An American military patrol opened fire on guards working at a building associated with the Supreme Judiciary Council, killing four and wounding one, the ministry official said. The circumstances of the shooting remained unclear. A bomb exploded in a crowded market in the New Baghdad neighborhood, killing one and wounding 22, the official said.

In Diyala Province, gunmen opened fire on two oil tanker trucks, igniting the trucks and killing five people inside, a provincial police official reported. Other gunmen killed a judge and his son in the provincial capital of Baquba, the police official said.

An American soldier died in what was called “a noncombat-related incident” north of Baghdad on Thursday, the American military said.

It said in another statement that Iraqi security forces operating about three miles from the Iranian border had “intercepted six heavily loaded donkeys.” The donkeys were hauling 53 Soviet- and Italian-made antitank landmines and one antitank projectile, which the troops confiscated and destroyed. No humans were captured, the statement said, and the donkeys were set free.