The paper also said on Thursday, quoting an army official speaking anonymously, that the three-month investigation led by Major General Eldon Bargewell is "also expected to call for changes in how US troops are trained for duty in Iraq".
The 24 civilians were killed on November 19 in the western Iraqi town of Haditha, hours after a US marine was killed by a roadside bomb.
Witnesses and rights groups say the marines raided three houses and shot five men in a car.
In his first public comment on the investigation George Bush, the US president, said on Wednesday that if wrongdoing was found, those involved would be punished.
"I am troubled by the initial news stories," he said. "I am mindful there is a thorough investigation going on. If in fact laws were broken, there will be punishment."
the Iraqi government announced on Thursday that it would launch its own investigation into the alleged killings.
The investigation will be carried out by a committee made up of the justice and human rights ministries along with security officials, an adviser to the prime minister, Nouri al-Maliki, said.
Homicide and false statement
In parallel with the Bargewell investigation, the Naval Criminal Investigative Service is conducting its own inquiry, which is expected to conclude this summer.
No charge has been filed, but people close to the case say charges of homicide, making a false statement and dereliction of duty are likely – among others.
"If in fact laws were broken, there will be punishment."
The Bargewell report is expected to be given to senior commanders by the end of the week. But even before that, the paper said the top US commander in Iraq, General George Casey, would order on Thursday that all US and allied troops undertake "new 'core values' training in how to operate professionally and humanely".
The Bush administration is still troubled by the torture scandal of Iraqi prisoners at the Abu Ghraib prison two years ago.
Several US troops were jailed.
One of Bargewell's conclusions is that the training of US troops for Iraq was inadequate, "with too much emphasis on traditional war-fighting skills and insufficient focus on how to wage a counterinsurgency campaign", the paper said, quoting the army official who asked to remain anonymous.
His report also shows that the killings in Haditha were not properly reported. The official declined to say whether he would describe the failure as a "cover-up".
The first failure lies in the false statement of Staff Sergeant Frank Wuterich, a squad leader who is believed to have been involved in the shootings.
He "made a false statement to his superior when he reported that 15 Iraqi civilians had been killed in the roadside bombing that killed a marine and touched off the incident", the paper said.
The other nine dead were initially reported by the marines as having been insurgents. The report was later changed - and publicly shared with journalists by an army spokesman - to eight insurgents killed and the other 16 Iraqis dying in crossfire.
A military spokeswoman told Time Magazine in January, when the paper started to make inquiries about the Haditha incident, that the insurgents had caused the civilian deaths by placing them in the marines' line of fire.
In March, Time broke the story that marines had killed civilians in Haditha.
Bargewell is expected to look into why the Marine Corps allowed statements by official spokespersons that were known to be false.
Another failure in reporting the incident was that the marines' unit that collected the 24 bodies "should have observed that the Iraqis were killed by gunshot, not by a bomb", the paper said.
Had it correctly reported what it saw, "that would have set off alarms and prodded commanders to investigate", the paper said, quoting its source.
The Marine Corps has put on hold the promotion of General Stephen Johnson, who was the top marine in Iraq at the time of the Haditha killings, to the rank of lieutenant-general, a senior Pentagon official said.
Also reflecting military unease before the Bargewell report's release, General Michael Hagee, the marine commandant, is visiting every marine post in Iraq.
Separately, the Marine Corps issued a directive to its generals telling them not to discuss details of the Haditha case.