BAGHDAD, Iraq (CNN) -- The number of U.S. military and Iraqi civilian deaths has dropped dramatically, according to recent reports, although American military officials said it is too soon to declare a turning point in the conflict.
Thirty-seven Americans have died in October, the lowest monthly figure since March 2006 when 31 perished, according to the U.S. military.
Three soldiers died Tuesday southeast of Baghdad when a roadside bomb struck a U.S. military patrol.
The number of Iraqi civilians killed in September was 844, down from 1,990 in January, according to Iraqi governmental figures provided to CNN.
Slain bodies found dumped in Baghdad dropped from 428 in August to 301 in September and 151 so far in October, the Iraqi Interior Ministry said.
The numbers mark a decline in fatalities since the war began in March 2003 and point to a decrease in violence after a year of pitched battles and sectarian strife.
Still, cautious U.S. and Iraqi military officials aren't ready to proclaim a decisive moment in the war, saying such an outlook would require the Iraqi government to do a better job of promoting political reconciliation and compromise.
"Well, I think we're almost there," said Lt. Gen. Raymond Odierno, the No. 2 U.S. commander in Iraq, interviewed by CNN. "I tell everybody we have momentum. We've not yet created what I consider to be irreversible momentum, but our goal is to create that irreversible momentum."
Iraqi Foreign Minister Hoshyar Zebari said, "We are in a race against time. We have to make the best use of time ... to step in before this achievement could evaporate."
Other examples of a decline in violence have emerged as well. Watch how a music store owner views the drop in violence »
An Iraqi commander, Lt. Gen. Abud Qanbar, said last week there have been steep decreases in attacks such as car bombings, terrorist operations against Iraqi security forces and civilians, and sectarian assassination attempts.
Iraqi and U.S. officials point to several factors contributing to this decline:
U.S. and Iraqi officials have been pointing to the rise of an anti-al Qaeda "awakening" among the Sunni tribes and a growing rejection of Sunni insurgents.
Rear Adm. Gregory Smith, a military spokesman in Baghdad, said progress made against al Qaeda in Iraq and other "criminal elements" has led to a drop in attack levels that has spurred "a decrease in casualties."
Along with the so-called surge, Odierno cited the improved performance of Iraqi security forces and Iraqis working together and "forgetting about the old hatreds."
Iraqi government officials said key compromises must be made among sectarian groups, such as accommodating more Sunnis in the Shiite-dominated Iraqi police and making economic and not just military improvements.
"One simple truth is that the government has to do a better job," Zebari said.
Sunni lawmaker Saleh Mutlaq, an outspoken critic of the government of Prime Minister Nuri al-Maliki, said the security situation is improving in Iraq, but might not last long.
"Well, it is improving, but my feeling is that this improvement is temporary because it doesn't reflect the presence of the American army and the Iraqi army volume in Baghdad and other cities."
Mutlaq added that the fight against al Qaeda is not over.
"Al Qaeda is very strong," he said. "It has been weakened in some areas but this weakness is only because the people of Iraq realize that al Qaeda is not good for them, especially the Sunni parts."
The Sunni lawmaker also attributed the improvement in security to Iraqis -- "especially the resistance" -- realizing that "the presence of the Iranians in Iraq is more important to fight than the Americans."
CNN's Jim Clancy, Jomana Karadsheh, Morgan Neil and Nic Robertson contributed to this report.