Lawyers are continuing to refer alleged abuse by soldiers to the  Iraq Historic Allegations Team (IHAT).
It has so far informed about 280 UK veterans they are under investigation.
No 10 said David Cameron feared people were being "solicited by lawyers" enticing them into making accusations.
Established in 2010 by the previous Labour government, IHAT has considered at least 1,515 possible victims, of whom 280 are alleged to have been unlawfully killed.
Unlawful death cases involving 35 alleged killings have already been referred to the Service Prosecuting Authority (SPA) - the military equivalent of the Crown Prosecution Service - along with 36 cases of alleged abuse and mistreatment with "multiple complainants".
Asked about reports that some servicemen had faced repeated investigation over the same events, the prime minister's official spokeswoman said: "We are deeply concerned about these types of situation.
"Every false claim that the government [has to] respond to, investigate and defend is diverting spending from the front line and from the work that our armed forces do to keep us safe.
"It is important that the government looks at what it can do to stop these types of scenarios where the claims may be fabricated, or not justified, and to look at how we deliver a better system in the future."
Two public inquiries have already looked at claims against UK troops in Iraq.
Last year, the Al-Sweady Inquiry concluded that allegations that troops murdered and mutilated Iraqis in custody were "wholly without foundation" - although some of the detention techniques used had amounted to mistreatment.
In 2011, another inquiry into claims of abuse highlighted the death of hotel worker Baha Mousa in British military custody, and blamed "corporate failure" at the Ministry of Defence for the use of banned interrogation methods in Iraq.
The PM's spokeswoman added: "We are concerned at reports about people being solicited by lawyers to make allegations that - as the Al-Sweady Inquiry showed - can often be fabricated."
She said IHAT's work should be "completed as quickly and efficiently as possible".
IHAT's budget of Â£57.2m runs until the end of 2019 - 16 years after the invasion of Iraq began in 2003.
Last week, the unit's head, Mark Warwick, said there were "lots of significant cases" being investigated and discussions would be held over whether any of them met the threshold for a war crimes prosecution.
Andrew Cayley QC, the director of the SPA, has said it "will not flinch" in prosecuting British soldiers where there is sufficient evidence of wrongdoing.
The Ministry of Defence says it takes such allegations "extremely seriously".
But Defence Secretary Michael Fallon has criticised "ambulance-chasing British law firms" whom he said were inhibiting soldiers on the battlefield because they feared being hauled in front of the courts on their return.
He argued there was "a strong case" for suspending the European human rights law when sending forces into action overseas.

The Binos parted company with McLaren on Saturday after a 4-0 home defeat to Elgin City.
That loss left them second bottom of Scottish League Two.
"No one could have worked harder than Stuart and I wish him every success in the future," said chairman Stuart Brown on the official website.
Former Stirling player McLaren was appointed boss in November 2014 following a spell managing Australian side Brisbane Strikers.
However, he could not save them from relegation, and they finished seventh last season.

Emergency services were called to reports of an incident at Daldowie Crematorium, off the M74, near Uddingston, at about 12:30.
The two men were taken to Wishaw General Hospital for treatment. There is no update on their condition.
Police said inquiries were ongoing and there was no truth in social media speculation about a firearms incident.
The prime minister is "deeply concerned" that Iraq War veterans could face threats of prosecution due to "fabricated" or "unjustified" claims of misconduct, Downing Street says.
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Stirling Albion have have appointed Martyn Corrigan as caretaker manager as they search for a replacement for Stuart McLaren.
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Two men have been taken to hospital following a disturbance at a crematorium in Glasgow.