The suspect, Rahmanullah Lakanwal, came to the US in 2021 under a programme that offered special immigration protections to Afghans in the wake of America’s withdrawal from Afghanistan.
President Donald Trump said the shooting underlined a major national security threat.
Edlow’s social media post on Thursday about the sweeping green card review did not explictly mention that attack.
“The protection of this country and of the American people remains paramount, and the American people will not bear the cost of the prior administration’s reckless resettlement policies,” said Edlow.
There were no further details about what the re-examination would look like.
The June proclamation his agency highlighted to the BBC set out an aim to restrict foreign nationals from entering the US to protect from “foreign terrorists and other national security and public safety threats”.
The administration said security concerns and the overstay rate of business, student and tourists visas were among the reasons for a country to make the list.
“The Taliban, a Specially Designated Global Terrorist (SDGT) group, controls Afghanistan,” the proclamation said. “Afghanistan lacks a competent or cooperative central authority for issuing passports or civil documents and it does not have appropriate screening and vetting measures.”
Other countries whose green card holders will undergo this examination include Burma, Chad, Republic of Congo and Libya.
The Wednesday attack on members of the US military prompted a forceful response from Trump.
“This attack underscores the greatest national security threat facing our nation,” the president said. “The last administration let in 20 million unknown and unvetted foreigners from all over the world, from places that you don’t even want to know about. No country can tolerate such a risk to our very survival.”
Last week, the same agency behind the green card review, the US Citizenship and Immigration Services, announced a review of all refugees admitted under former President Joe Biden.
On Wednesday, the US suspended processing all immigration requests from Afghans, with Citizenship and Immigration Services saying the decision was made pending a review of “security and vetting protocols”.