Mark Warwick said there were "lots of significant cases" and that discussions would be held over whether they met a war crimes threshold.
Lawyers are continuing to refer alleged abuse by soldiers to the Iraq Historic Allegations Team (IHAT).
The Ministry of Defence said it took such allegations "extremely seriously".
Mr Warwick, a former police detective who is in charge of IHAT, told the Independent that the allegations being investigated included ones of murder.
The inquiry has considered at least 1,515 possible victims, of whom 280 are alleged to have been unlawfully killed.
Mr Warwick said: "We would look at the credibility of the allegation in the first instance and, when we've looked at a lot of these extra cases coming to us, some of them are duplicates of cases, some of them we've already identified as part of our own investigation process, and some are multiple allegations, where we would investigate as a single allegation."
IHAT's budget of £57.2m runs until the end of 2019 - 16 years after the invasion of Iraq began in 2003.
"Over the next 12 to 18 months, we will review all the caseload to better understand the picture and then I think we can say whether 2019 seems realistic," said Mr Warwick.
BBC political correspondent Chris Mason said Mr Warwick's comments may have been a response to an interview by Michael Fallon reported in the Telegraph.
In it, the defence secretary said soldiers were inhibited on the battlefield because they feared "ambulance-chasing British law firms" would haul them in front of the courts on their return.
Public Interest Lawyers, which represents some alleged victims, said IHAT was "failing to investigate" those responsible for "systemic" abuse.
"Despite public inquires, court proceedings ongoing since 2004 and the IHAT team of investigators, there is yet to be a single prosecution resulting from IHAT's work," a spokesman said.
Carla Ferstman, director of the human rights charity Redress, told the Independent that the "incredibly slow pace" of IHAT's investigations was "wholly unacceptable".
She added: "Things seem to still be moving at a snail's pace. We call upon the government to ensure IHAT can, and does, do what it was set up to do, and to do it now. This cannot be a whitewash."
Col Richard Kemp, a former army commander in Afghanistan, agreed that the investigation needed to be completed urgently, but said it was "inconceivable" that that number of allegations against British troops could be legitimate.
"Of course one has to be concerned about these allegations, but the number, the sheer number, thousands of allegations made against British soldiers in Iraq, I just cannot believe that any significant number of them can be valid," he told BBC Radio 4's Today programme.
However, Dr Andrew Williams, from the University of Warwick, said the investigations could take "some years more", saying the process could "drag out for a long time to come".
Dr Williams - who has written about the murder of Iraqi civilian Baha Mousa - said the "lapse of time" since the alleged crimes could hamper investigations.
"In terms of obtaining the witness testimony from the Iraqi civilians concerned, that will be tricky. They are obviously still based in Iraq and getting hold of them, interviewing them, is a long process and logistically very difficult."
A Ministry of Defence spokeswoman said: "The vast majority of UK service personnel deployed on military operations conduct themselves professionally and in accordance with the law.
"Where there is sufficient evidence, members of HM Forces can be prosecuted."
An inquiry into claims of abuse by UK troops in Iraq highlighted the death of 26-year-old hotel worker Mr Mousa, who died in UK military custody in September 2003.
It concluded in September 2011, with inquiry chairman Sir William Gage blaming "corporate failure" at the Ministry of Defence for the use of banned interrogation methods in Iraq.
The Al-Sweady Inquiry, set up in 2009, followed allegations made in judicial review proceedings at the High Court that the human rights of several Iraqis were abused by British troops in the aftermath of a firefight with insurgents near the town of Majar al-Kabir.
Inquiry chairman Sir Thayne Forbes said allegations that troops murdered and mutilated Iraqis in custody were "wholly without foundation". But he did conclude that some of the detention techniques had amounted to mistreatment.