By Jim Acosta, Sara Murray and Maegan Vazquez, CNN

(CNN) -- It was a mistake for the Trump administration not to leave the door open to purchase more Pfizer coronavirus vaccine doses earlier this summer, an administration official told CNN on Monday.

The admission comes even as the White House has denied they turned down an offer to procure more vaccine doses earlier this year and ahead of President Donald Trump's executive order signing aimed at prioritizing the shipment of the coronavirus vaccine to Americans before other nations.

The official added that the US simply may have to hope that the other vaccines being produced by other companies are just as effective as the Pfizer doses.

"They shouldn't have closed the door," the official said, adding that "they could have left the door open" to purchasing more doses.

If the other vaccines being manufactured by Pfizer's rivals are not as effective, it could have a detrimental effect on inoculating the American public, the official said.

"It's going to look bad," the official added.

On Monday, some senior administration officials denied reports that the administration passed on the Pfizer offer, and White House press secretary Kayleigh McEnany echoed that denial to CNN's Joe Johns on Tuesday morning.

But her deputy press secretary, Brian Morgenstern, told Fox News later Tuesday that there were "options" with Pfizer under discussion, but that the talks didn't get into the details of the potential purchase.

"When we went to discuss exercising those options, we never got to whether we'd have one dose or 100 million, whether it would be tomorrow or 10 years, so when we're in that kind of status, I think it's disingenuous to say there was an offer there that we really could have accepted moving forward," Morgenstern said.

The official familiar with the situation confirmed that Trump administration officials passed up a chance to purchase more than the 100 million doses of Pfizer's vaccine it agreed to earlier this summer. The decision was made as part of a plan to "diversify" the nation's vaccine arsenal, the official said, adding that members of the administration's "Operation Warp Speed" effort to mass produce a coronavirus vaccine were trying "not put all their eggs in one basket."

Dr. Scott Gottlieb, a former commissioner of the US Food and Drug Administration, also told CNBC something similar, adding that he believes the government "made a bet" that they could potentially purchase vaccines from multiple manufacturers, not just Pfizer.

The decision to not purchase more Pfizer doses, which was first reported by The New York Times, has mounted concerns that the company would be unable to fulfill any additional US order until June because of their commitments to other countries.

A senior administration official told CNN that one of the primary reasons the US did not exercise the option to buy additional doses of the Pfizer vaccine was because the company could not commit to a specific number of doses and a timetable for delivering them.

Without a firm delivery date or quantity -- and with other vaccine candidates in the works as well -- the US held off on placing the order for additional doses.

The official that said even before Pfizer's phase three clinical data was available, Operation Warp Speed officials had been inquiring with Pfizer about committing to a firm delivery date for doses beyond the initial 100 million the US purchased earlier this year.

The official added that negotiations are still continuing and said "it's a shame that it seems that some people want to try to turn this negotiation public."

Pfizer declined to comment on the timeline issues, pointing to an earlier statement from company spokeswoman Amy Rose that said: "Any additional doses beyond the 100 million are subject to a separate and mutually-acceptable agreement. The company is not able to comment on any confidential discussions that may be taking place with the US government."

The debate about whether to buy additional doses of the Pfizer vaccine was also never raised with the White House coronavirus task force last summer -- another sign of the lack of transparency around Operation Warp Speed even within the Trump administration, according to a separate person familiar with the matter.

While Operation Warp Speed was working closely with Health and Human Services and Secretary Alex Azar, it kept its operations so tightly held that even members of the task force were often in the dark about vaccine development and procurement plans, the person said.

Moncef Slaoui, the chief scientific adviser of Operation Warp Speed, said that summer was not the time to buy more vaccine doses -- and that the right time to do that is when it becomes clear how well the vaccines perform.

"Let me remind everybody what our strategy is and has always been," Slaoui told ABC News anchor George Stephanopoulos on "Good Morning America" on Tuesday. "We selected six different vaccines to build the portfolio, to manage the risk that some may work and some may not work, but also to ensure that as more than one would work that we would accumulate vaccine doses from this portfolio of vaccines."

Slaoui said that during the summer, "(i)f somebody came to us and said, 'Let's buy more of this vaccine or that vaccine,' no one reasonably would buy more from any one of those vaccines because we didn't know which one would work and which one may be better than the other."

Slaoui also refused to weigh in on Trump's forthcoming executive order.

"Frankly, I don't know -- and frankly, I'm staying out of this, so I can't comment," Slaoui told Stephanopoulos.

Stephanopoulos pressed Slaoui, asking, "You don't know? But you're the chief science advisor for Operation Warp Speed?"

"Our work is, you know, rolling. We have plans we feel that we can deliver the vaccines as needed, so I don't know exactly what this order is about," Slaoui responded.