There is no known precedent for a president to make such a decision for anyone seeking a security clearance, according to security experts.
The deadline for stripping officials of their interim clearances was Friday, though it wasn't clear by late in the day what specific action had been taken.
Trump told reporters on Friday that Kelly would make the final decision as to any exception for Kushner.
Kushner's attorney, Abbe Lowell, said the new policy would "not affect Mr. Kushner's ability to continue to do the very important work he has been assigned by the president".
White House security clearances were thrust front-and-center this month following the departure of Trump's former staff secretary Rob Porter. But while effusive in his praise for Kushner - labeling him an "extraordinary dealmaker" - the president said he wouldn't decide whether his senior adviser retains access to classified information. "General Kelly respects Jared a lot and General Kelly will make that call", Trump said at a news conference.
Kushner is now working at the White House with a temporary security clearance and felt personally targeted by Kelly's decision.
A White House spokesman declined to comment on the status of Kushner's clearance or on information relayed by Rosenstein to McGahn.
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Trump also complained he'd inherited a "broken" background check system in which it can take "months and months and months" for full security clearance to be granted, even for people without complicated financial holdings.
Options included giving Mr. Kushner a lesser clearance that would allow him to keep doing his job. One other said Rosenstein did not discuss the nature of the ongoing investigation. But Vanity Fair says that by issuing a red line, Kelly has pulled off a "political masterstroke" by training more spotlight on the president's ethics, which will endure whether he stays or goes.
As of November, White House counsel Don McGahn - who has also been interviewed by Mueller's team - had received a Top Secret clearance, but was still working off interim access to SCI.
"It seems to me that he should have restricted access to highly classified material until the resolution of those issues", Bauer said.
Administration officials have tried to portray the delay in Kushner's security clearance as normal, and told Politico that high level administration officials who require the highest clearance undergo heightened scrutiny.
"It shouldn't take this long", Trump said, apparently referring to the process of receiving a permanent security clearance.