Aws Mohammed Younis Al-Jayab in 2012 was among the first Iraqi refugees to enter the U.S. after President Obama lifted a six-month freeze on such entries as his aides tightened a shaky vetting process.

Once on U.S. soil, it took Al-Jayab a matter of weeks to embrace terrorism. He began chatting on social media about his support for the Islamic State and bragging about the killings he committed in Syria. By November 2013, he was on his way back to Syria to fight for one of the bloodiest terrorist groups in history.

In Syria, he posted: “America will not isolate me from my Islamic duty. Only death will do us part.” After fighting in Syria, he returned to the U.S. in January 2014 and settled in Sacramento, California.

Al-Jayab twice cleared what was supposed to be an improved vetting procedure.

Today, Al-Jayab could be cited as justification for President Trump’s executive order to suspend immigration from Iraq and six other Muslim-majority nations that the Obama administration singled out as high-risk for terrorist infiltration. Trump officials say the administration wants to revamp the screening process and assess the accuracy of personal histories it receives from those seven countries.

“Obama’s vetting procedures were a dismal failure,” said Robert Spencer, director of the nonprofit Jihad Watch. “There is no reliable way to distinguish jihad terrorists from peaceful refugees. The choice is either to keep out some legitimate travelers or to allow in some jihad mass murderers. There is no viable third alternative.”

Al-Jayab, whom the Justice Department indicted in January 2016 on charges of lying to the U.S. government, is not the only bogus refugee welcomed to America after the 2011 entry freeze.

In 2013, Al-Hamzah Mohammad Jawad arrived as an Iraqi refugee. Two years later, he was arrested as he boarded a flight for Jordan to join the Islamic State. He had been learning how to fire a gun and said a uniform was waiting for him in Iraq.

Sen. Jeff Sessions, Alabama Republican and now attorney general nominee, released a staff investigative report last year that said at least 40 refugees allowed entry into the U.S. have been implicated in terrorism since the Sept. 11, 2001, al Qaeda attacks.

Critics of Mr. Trump’s suspension of immigration argue that the terrorists’ infiltration of Middle East and North African refugees in Europe has not occurred here. Mr. Sessions’ list rebuts that argument to some degree.

White House press secretary Sean Spicer said Monday that the president does not want to wait for a rash of terrorist attacks before acting to improve the refugee vetting system.

“We know that at least 40 individuals who were admitted to the United States as refugees have been convicted for, or implicated in, terrorism or terrorism-related offenses — and the total is likely much higher,” said Mr. Sessions, chairman of the Senate Judiciary subcommittee on refugees. “Some were admitted as adults, others as children, but these cases refute the false assertion that those admitted to the United States as refugees never engage in terrorism. But because these facts do not fit within his worldview, President Obama rejects them. And in so doing, he rejects his sacred oath for what he perceives as political gain.”

Mr. Sessions uttered those harsh words while supporting Mr. Trump in the presidential race and while Mr. Obama was moving to accept thousands of Syrian refugees.

To critics who wanted a pause and more strenuous vetting of refugees, Mr. Obama said, “That’s not who we are.”

Mr. Sessions’ staff backed up his statistics with snapshots of 20 refugees implicated in terrorism who were vetted by the Bush and Obama administrations.

The Sessions list does not include two of the most notorious terrorists: Dzhokhar and Tamerlan Tsarnaev, whose pressure-cooker bombs during the 2013 Boston Marathon killed three and injured hundreds. The brothers entered the U.S. after their father gained asylum.

Some of the 20 refugees “fully vetted” by the U.S. government:

• Bilal Abood, an Iraqi translator for U.S. troops, who was sentenced on May 25 to four years in prison for lying to the FBI. He entered the U.S. via a special visa program for translators in 2009. He sneaked out of the U.S. via Mexico, traveled to Syria and joined the Islamic State group. His computer showed he pledged an oath to Islamic State leader Abu Bakr al-Baghdadi.

• Fazliddin Kurbanov, who arrived as a refugee in 2009. He was convicted of conspiring to help the Islamic Movement of Uzbekistan and had acquired bomb-making materials to kill people in the U.S.

• Somali refugee Abdurahman Yasin Daud, who was charged with six others in Minnesota with providing support to the Islamic State. He drove from Minnesota to San Diego and tried to acquire a passport to enter Mexico and travel to Syria.

• Abdinassir Mohamud Ibrahim, who came to America in 2007 from Somalia. He lied to win refugee status, claiming he was part of a persecuted clan in Somalia when he was not. In the U.S., he provided material support for the al Qaeda-linked al-Shabab. He was sentenced to 15 years in prison.

• Liban Haji Mohamed, who drove a cab in the District of Columbia area and has a U.S. arrest warrant for helping al-Shabab. He arrived from Somalia as a refugee and became a U.S. citizen. He is believed to have sneaked across the U.S.-Mexico border. The FBI considers him an asset to terrorist groups that want to pick targets in the nation’s capital.

Mr. Obama suspended the Iraqi refugee program based on a specific terrorism case. Two Iraqis who worked to kill American troops in Iraq were admitted to the U.S. as refugees.

Iraqi Waad Ramadan Alwan entered the U.S. in 2009 and settled in Kentucky. In 2011, he pleaded guilty to 23 charges of conspiring to kill American troops in Iraq as a member of al Qaeda in Iraq, which eventually became the Islamic State. His fingerprints were found on undetonated improvised explosive devices, the prime killer of U.S. personnel.

He bragged to an FBI informant about how many Americans he had killed, calling them his “lunch and dinner.” Alwan was sentenced to 40 years in prison on Jan. 29, 2103, in a federal court in Kentucky.

That same day, in the same court, another Iraqi refugee — Mohanad Shareef Hammadi — was sentenced to life in prison for serving in al Qaeda in Iraq.