But his claim is being undercut by revelations that 30 to 40 people in the White House have yet to secure permanent security clearances a year into the administration and could potentially be unsuited to such high-level jobs.
The extent of the backlog emerged in a CNN report Friday that coincided with uproar over the departure of White House aide Rob Porter, who was confined to an interim clearance, after two ex-wives told the FBI he abused them.
The episode again raised the issue of whether some of Trump's picks for key White House jobs -- including his son-in-law and foreign policy fixer Jared Kushner, can be trusted to deal with highly classified information.
The new focus on security clearances also compounded previous worries that the inexperience of the Trump team, extensive business entanglements and its unconventional approach to politics meant that it was a poor fit for the responsibilities of the highest offices.
Personnel questions also flared after months of incessant feuding between top White House officials and a dizzying sequence of West Wing resignations and firings, not to mention charges slapped on four former Trump associates by special counsel Robert Mueller.
"This administration and indeed Trump's team before the campaign, during the campaign and now in the White House, includes people who are totally unfit to handle classified information," said Evan McMullin, a former CIA officer who briefly ran as an independent presidential candidate in 2016.
McMullin said some Trump appointees were having trouble getting clearances because of associations with foreign governments hostile to the US, or through personal habits -- like Porter for instance -- that could potentially leave them vulnerable to blackmail by foreign agents.
"Sadly, Trump and his team are poorly suited to handle information like this and this is why getting clearances for members of his team is difficult," McMullin told CNN on Saturday.
The White House hit back hard on Monday, effectively blaming the FBI for the backlog in the clearance process.
"I can tell that you we do rely on the same process that has been used for decades," White House press secretary Sarah Sanders told reporters.
"And if changes are thought to be made, that would be made by the law enforcement and intel communities that run that process, not the White House. "But that's something that could be looked at, certainly, in light of this."
Multiple White House officials later said that the line was not an attack against the intelligence community -- something the administration has done from time to time -- but more a reflection that people are "asking us to fix a process that we have no say so in fixing."
"It's never been a White House issue. It's always the outside entities who conduct these investigations," the official said.
But several sources, including intelligence officials who have served in Democratic and Republican administrations told CNN last week that such a backlog was very unusual and made clear the process should have been finished after a year in office.
Nada Bakos, a former CIA analyst said Monday that a year was a "long time" for permanent clearances to still be outstanding.
"We all know there is a backlog at various levels for security clearances but these are people in the White House ... We are talking about the suitability of the people they have put into these positions, that is what I think is at question," Bakos told CNN's Brooke Baldwin on Monday.
The White House insisted it had no greater priority than safeguarding America's secrets, and Sanders lashed out at the press, slamming the publication of leaks that put "national security at risk."
"Frankly, if you guys have such concern with classified information, there's plenty of it that's leaked out of the hill, that's leaked out of other communities well beyond the White House walls," Sanders said.
The comment was ironic given that Trump recently declassified intelligence information in a Republican memo apparently aimed at discrediting the Mueller probe, despite public objections of his own FBI and Justice Department.
The White House record in safeguarding intelligence has also been dubious on several occasions. Former national security adviser Michael Flynn served in the administration for several days after the White House was warned he could be compromised after laying to the FBI over conversations with Russian officials.
And Trump himself reportedly disclosed classified information to several top Russian officials in an Oval Office meeting last May.
'Dozens' yet to be cleared
A source knowledgeable about the background clearance process inside the White House said that there were "certainly dozens, maybe even more" people yet to be cleared inside the administration who are operating on interim clearances.
"What happens is they do the easy ones first," the source said, noting that many lower level, young people who have never been checked before but don't have an extensive histories of foreign travel or contacts have been cleared.
More senior figures, such as Kushner, who has played a vital role as a liaison between Trump and key allies like Israel and Saudi Arabia, and was influential early on in China policy are still being held up.
Kushner has made numerous updates to his security clearance questionnaire, known as a SF-86, partly because of his failure to initially disclose some meetings with foreign officials. Democrats responded by demanding the withdrawal of his privileges to view classified information.
Another source knowledge of the process said that it was not uncommon for "higher-level" clearances to take longer as such candidates generally have deeper backgrounds with more contacts and questions that need to be asked.
This person said there were "certainly dozens, maybe even more, yet to be cleared" inside the Trump administration, but that those people who have yet to secure full security clearance are on interim clearance.
Trump's status as a Washington insider who had never held public office nor served in the military could also be a factor as he has tried to build a governing team in his own image. But in the process, he has also chosen officials with long histories of foreign business contacts and potential conflicts of interest likely to be flagged in the clearance process.
Other, more conventional Republican operatives, who may be less exposed have either decided not to serve or have been blacklisted for opposing Trump.
"There are still a lot of people who have said that they are unwilling to work in the White House and there are a lot of people that the White House is unwilling to have come in," said longtime Republican operative Doug Heye.
Though he added that he thinks Trump's current team is "all qualified people who are trying to do the best for their country," he added that it may be hard to find a stable of people waiting in the wings to take over for them.
That exasperates the Trump administration's difficulties, with a recent Brookings Institution report citing 34% staff turnover for Trump's first year, triple what it was in the Obama administration and double what it was in the Reagan administration for the same time period.
Many GOP foreign policy experts for instance endured a period of soul-searching as they considered whether they could stomach serving a disruptive force like Trump who repudiated decades of Republican strategic orthodoxy.
Others made the decision to serve in the government, reasoning that the inexperience of the Trump team meant they had a patriotic duty to join up.