BAGHDAD — The monthly toll of American service members who have died in Iraq is on track to being the lowest in nearly two years, with at least 37 troop deaths recorded as of today, but the military cautioned it’s too early to declare a long-term trend.

Iraqi civilians, meanwhile, faced more attacks today.

At least four mortar rounds slammed into a village near Saddam Hussein’s hometown of Tikrit, killing a woman and wounding five other civilians, police said.

In Baghdad, gunmen in a speeding car tossed a hand grenade into a crowd of shoppers in eastern Baghdad, killing one person and wounding five, according to an officer in the capital. The officials spoke on condition of anonymity because they weren’t authorized to release the information.

At least 37 American service members have died so far in October, nearly a quarter from non-combat causes. Among them were three soldiers killed today when a bomb exploded as they patrolled southeast Baghdad, the military said.

It is the lowest number since 32 troops died in March 2006 and the second-lowest since 20 troop deaths in February 2004, according to an Associated Press count based on military figures.

That would be the second consecutive drop in monthly figures, after 65 Americans died in September and 84 in August.

In all, at least 3,843 members of the American military have died since the Iraq war started in March 2003, according to the AP count.

A military spokesman in Baghdad, Major Winfield Danielson, pointed to a number of likely reasons for the decline, including an American security push that has driven militants out of former safe havens and a change in strategy that has placed troops closer to the population. That, in turn, has caused a rise in the number of tips from residents about roadside bombs and other dangers.

He also singled out the cease-fire call by a radical Shiite cleric, Muqtada al-Sadr, who in August ordered his fighters to cease attacks against American-led forces and other Iraqis for up to six months. Major Danielson said Iraqi forces also were increasingly taking charge of security operations.

He welcomed the lower numbers but stressed it was too early to say it was a downward trend.

“Have we turned a corner? It might be a little too early to say that,” he said. “It’s certainly encouraging.”

In August, the American Army expressed concern that repeated deployments and tours of duty that have been stretched to 15 months were putting increasing pressure on military families and creating record suicide rates among soldiers.

There were 99 Army suicides last year — nearly half of them soldiers who hadn’t reached their 25th birthdays, about a third of them serving in Iraq or Afghanistan.

The 2006 total — the highest rate in 26 years of record-keeping and the largest raw figure in 15 years — came despite Army efforts to set up new programs and strengthen old ones for providing mental health care to a force stretched by the longer-than-expected conflict in Iraq and the global counterterrorism war entering its sixth year.

The current pace of civilian deaths also would put October at less than 900. The figure last month was 1,023 and for August, 1,956, according to figures compiled by the AP from hospital, police, and military officials, as well as accounts from reporters and photographers. Insurgent deaths are not included. Other counts differ and some have given higher civilian death tolls.

Suspected Sunni and Shiite extremists appear to have stepped up attacks in recent weeks, however.

A suicide bomber rode his bicycle into a crowd of police recruits in
Baqouba, killing at least 29 people in a province that has become a
battleground among American forces, Al Qaeda militants and Shiite radicals.

A group of Shiite and Sunni tribal leaders, meanwhile, were rescued yesterday, one day after they were kidnapped in the capital after meeting with the government to discuss how to coordinate efforts against Al Qaeda in Iraq. A Sunni sheik who was among those abducted was killed.

Clashes also erupted for more than four hours yesterday as American forces battled Shiite militia fighters near Mr. al-Sadr office in the predominantly Shiite northwestern Baghdad neighborhood of Hurriyah. Before the clashes, witnesses described militia fighters wielding weapons in the streets, which were blocked to outside access.

An American brigadier general was wounded in a roadside bombing yesterday in northern Baghdad, the military reported, but it could not be determined if that was connected to the fighting.

A commanding general of the Gulf Region Division, Brigadier General Jeffrey Dorko, was the highest-ranking American officer to be hurt since the conflict began in March 2003. General Dorko was in stable condition and was evacuated to Landstuhl Regional Medical Center in Germany; his injuries were not life-threatening.