Washington (CNN) White House chief of staff John Kelly, facing a growing swell of internal strife , attempted Wednesday to bring a spiraling crisis under control even as morale has plummeted among West Wing aides who feel misled and leaderless.

Furious at leaks depicting him as a liar, Kelly planned to directly confront the issue during a morning staff meeting, people familiar with the matter said. Later, officials said the regular Wednesday staff meeting did not take place because Kelly was meeting with senators, but he had individual conversations with people in the West Wing in hopes of restoring confidence.

Kelly was expected to strike a more conciliatory tone than he did at a similar session last week, when he claimed that he'd acted swiftly to fire Rob Porter, the former staff secretary accused of abusing his ex-wives. White House staffers walked away from that session believing Kelly was asking them to lie.

This time around, Kelly was expected to acknowledge to some aides -- as two White House spokesmen have conceded from the briefing room -- that some things could have unfolded differently, the sources said. But he will insist that staffers come into line instead of airing their grievances in the press.

Even as President Donald Trump continues to express confidence in Kelly -- and did so again Wednesday through a spokeswoman -- that has done little to quiet the clamor about the standing of the chief of staff.

It's an unfamiliar situation for the ordinarily hard-nosed retired Marine general, who has insisted upon military-like rigor in the West Wing. Normally unflappable, Kelly has this week seemed chastened by the mounting blowback, people familiar with his attitude say. He has tried striking a more friendly tone with staff, the people said.

Kelly is facing growing anger among his ranks that the matter was handled ineptly, and that more wasn't done to prevent an accused abuser from swiftly rising in rank. CNN reported on Tuesday that Porter was due to be promoted before resigning amid the abuse allegations. Testimony from the FBI director on Tuesday that contradicted Kelly's version of events only heightened the sense that his standing is increasingly precarious.

"Who knew what when, and if you knew it in 2017 and the bureau briefs them three times, how in the hell was still he employed?" Gowdy said on "New Day."

Later Wednesday, Vice President Mike Pence defended Kelly, saying he had done "a remarkable job" and he looks forward to "continuing to work with him for many, many months to come."

Damaging headlines

Trump has himself expressed frustration that Kelly hasn't been able to tamp down on the deeply damaging headlines, though does not blame him entirely for the current state of affairs, according to a person familiar with the matter. Kelly, meanwhile, has blamed the White House communications operation for mishandling the fallout.

Other top aides have also come under internal scrutiny over their handling of the situation. White House counsel Don McGahn and deputy chief of staff for operations Joe Hagin have both been privately blamed by colleagues for not taking action to suspend or dismiss Porter when they first learned of the possible allegations last year.

As he does periodically, Trump has been quizzing informal friends and advisers about possible replacements for Kelly. The President has long expressed some frustration with Kelly for imposing a strict system that rubs against Trump's freewheeling nature.

Sources have told CNN those conversations heated up over the past week , with talk centering on White House chief economic adviser Gary Cohn, House Majority Leader Kevin McCarthy and White House budget director Mick Mulvaney as possible successors.

But according to two people familiar with the President's calls, he has not indicated that he's ready yet to dismiss Kelly. He's expressed misgivings about changing his staff before high-stakes immigration legislation is hammered out, according to one of the people. Kelly has helmed talks with lawmakers on a possible agreement.

Kelly himself told colleagues in the White House on Tuesday evening that the rumors of his demise were "not true," according to a person familiar with the situation.

And Trump has a long history of allowing aides who have disappointed or angered him -- such as Attorney General Jeff Sessions -- to twist in the wind without firing them outright.

Standing by Kelly

Despite multiple aides blaming him for the bungled response, the White House was standing by Kelly as of Wednesday morning. Asked if Trump has confidence in his chief of staff, White House press secretary Sarah Sanders said "Yes."

And some close to the President dismissed the swirl of chief of staff rumors as the work of conniving members of Trump's extended orbit, who have long resented Kelly for cutting off access to the Oval Office.

A person who spoke to Trump on Tuesday night said the President himself wondered where some of the rumors were originating.

"Where is this Gary stuff coming from?" he asked, referring to Cohn, a Democrat and former Goldman Sachs executive who has clashed with Trump in the past over his equivocal comments about racist violence in Virginia.

The answer, according to several sources familiar with the matter, was from Jared Kushner and Ivanka Trump, the President's senior advisers and children, who have pressed Cohn's case internally. Both are said to be furious over Kelly's handling of the Porter matter.

A person close to Cohn says there is little doubt he would take the job if asked. But the blowback from conservatives and right-wing media — including Breitbart, which has criticized Cohn in the past -- would undoubtedly be fierce.

"It would drive a final stake in everything (Steve) Bannon built," the person close to Cohn said.

Many inside the West Wing view the chief of staff rumors as largely a trial balloon fueled by Kelly's critics, who see the Porter crisis as a possible opening. A White House official said the President is feeling out potential candidates only if he decides to replace Kelly, a possibility that remains far from certain.

As the scandal entered a second week, Kelly hasn't demonstrated any signs he's withdrawing. He attended several meetings with the President on Monday and Tuesday.

On Wednesday, he arrived at work after Ash Wednesday mass, still wearing the black ash cross on his forehead.

CNN's Elizabeth Landers and Abby Phillip contributed to this report.