The Obama administration is trying to allay growing public fears that the thousands of Middle Eastern refugees it’s resettling in America — virtually all of whom are Muslim — pose a terrorist threat to the homeland.

Top US officials insist there’s no evidence refugee applicants who go through the U.S. screening process pose a greater security threat than members of any other immigrant group. They claim they are rigorously vetted for terrorist and criminal ties, and that resettlement communities throughout the US are safe.

“There is absolutely no evidence, my friends, zero evidence, that refugees who make it through this arduous process, pose any greater threat to our society than the members of any other group,” Secretary of State John Kerry said while visiting a Washington-area mosque recently.

“And it is important for people to know that,” he added, so they refrain from leveling “bigoted and hateful rhetoric” against the Muslim refugees.

But the secretary deserts the truth. The evidence is overwhelming that even known, hardened terrorists make it through the supposedly “arduous” process.

Perhaps the most egregious example is that of Iraqi refugees Waad Ramadan Alwan and Mohanad Shareef Hammadi, two known al-Qaida terrorists who skated right through the administration’s supposedly rigorous screening program within months of each other. They were resettled in Nevada and Kentucky, despite being detained by authorities in Iraq for planting bombs that killed U.S. soldiers and despite having their fingerprints on file in a bomb database.

It’s instructive to examine their case in greater detail, because it shows just how dangerously flawed the U.S. refugee screening system is.

These weren’t refugees from war-torn Syria, where authorities have no reliable database of information to screen immigrants flooding the U.S., no terrorist or even criminal record of them.

Rather, Alwan and Hammadi came from Iraq, another ISIS hotspot, but where the U.S. has a large embassy and a client government, and a lot more information about refugee applicants. U.S. soldiers and military intelligence officers had operated in Iraq for several years, a much different story than in neighboring Syria, where there are few boots on the ground. They had detained and investigated bad guys on a daily basis in Iraq, collecting information on thousands of individuals and sharing it with the FBI, Homeland Security and the State Department.

In fact, plenty of derogatory information was collected on Alwan and Hammadi. Yet the U.S. refugee admissions program still failed to screen out these jihadi killers as security threats.

From 2003 until his capture by Iraqi authorities in May 2006, Alwan fired sniper rifles at U.S. forces and placed hundreds of IEDs in roadways to blow up Humvees and Bradley fighting vehicles, as a member of al-Qaida in Iraq, the precursor to ISIS. Government documents reveal he bragged about how he and other insurgents “fucked up” Hummers and U.S. personnel with hidden bombs filled with ball-bearings, nails and gravel. He said that he had American soldiers for “lunch and dinner.”

Hammadi, for his part, also participated in IED attacks on US forces as a member of al-Qaida in Iraq. An experienced and well-known insurgent, he had been arrested not once, but twice by Iraqi authorities, according to an FBI affidavit.

In other words, both Alwan and Hammadi had long rap sheets and were on the radar of Iraqi and US intelligence. Alwan was even tracked crossing the border into Syria.

Yet both passed background checks and were declared “clean” by US immigration and security officials who followed the administration’s “arduous” refugee screening procedures.

Alwan entered the US in April 2009 and was resettled in Bowling Green, Ky. Hammadi entered the US in July 2009 and took up residence in Las Vegas before being moved to Bowling Green, where he soon reconnected with Alwan.

The pair of jihadists sought asylum as Iraqi war refugees, when in fact they were the enemy. As sympathetic refugees, they were invited to receive welfare and move into public housing, which happened to be located near high-security Fort Knox and Fort Campbell, where the army Nightstalker pilots involved in the raid on Osama bin Laden were based.

Their hatred for America — “I didn’t come here for America” but for “jihad,” Alwan stated — soon became apparent. Alwan spoke of targeting an Army captain in the US and possibly attacking other homeland targets.

The FBI began conducting undercover surveillance of Alwan and Hammadi, using a confidential informant to help spy on them. Agents soon learned that Alwan’s work at a power plant in Iraq was just cover. He was really a terrorist who worked as a sniper and bomb-maker targeting Americans on a daily basis.

One day, they overheard Alwan describing an IED consisting of three high-explosive artillery rounds that he helped build and plant in a roadway near Bayji, Iraq, in 2005. He said he regretted that it failed to detonate, noting in a conversation with the confidential source that he used a particular brand of remote cordless telephone base station to assemble the bomb.

The FBI investigated and found out the bomb had been recovered by US forces. In January 2011, analysts with the FBI’s Terrorist Explosive Device Analytical Center were able to identify two latent fingerprints belonging to Alwan on the Senao brand phone component.

It confirmed case agents’ fears: a terrorist with serious bomb-making skills had infiltrated the U.S. as a refugee.

How could they wrap him up before he could attack Americans inside America? Problem was, Alwan and his co-conspirator Hammadi were here legally, aided, sheltered and protected by the State Department’s generous refugee program.

The FBI decided to set up a sting operation, enticing both suspects to participate in a terrorist scheme to procure and ship weapons — including sniper rifles, machine guns, rocket-propelled launchers, Stinger missiles and C4 pastic explosives — to al-Qaida in Iraq.

The trap worked. Alwan even drew several diagrams of IEDs to help the “mujahidin” kill US troops.

Luckily, both Alwan and Hammadi were put away for 40 years in 2013 for providing material support to al-Qaida. But how many more like them are out there plotting? Alwan spoke of “other cell members” in Bowling Green. And how many additional terrorists-posing-as-refugees are slipping through the net right now?

Maddeningly, the FBI overheard Alwan in one conversation say the he could not go back to Iraq because “I am wanted there.” Yet he was welcomed here with open arms.

While Iraqi refugees are hard enough to screen for terrorist ties, FBI Director James Comey testified last year that it is virtually impossible to conduct background checks on Syrian refugees. “We have no information” on them, he warned.

Yet the State Department is on track to meet President Obama’s target of resettling 10,000 Syrian refugees in cities across America during fiscal year 2016.

Last month, the number of Syrian refugee admissions surged to more than 2,380 — more than double the number the State Department resettled in the U.S. in May.

A recent poll of 900 Syrian refugees by the Arab Center for Research and Policy Studies found that as many as 23% — or almost 1 in 4 of them — could be susceptible to ISIS recruitment.

That means as many as 2,300 of the 10,000 Syrian refugees that Obama is resettling inside American cities are potential terrorist threats.