A former political director to President George W. Bush said Wednesday she found the news of James Comey's firing "dumbfounding."

"Even if you assume that their intentions were pure, and they fired him because of competence reasons, this just stinks to high heaven," Sara Fagen, a CNBC contributor, said on "Squawk Box."

Also on the show, former CIA agent John Sipher said Comey's firing likely won't end the FBI's investigation into possible links between Russia and President Donald Trump's campaign.

The Trump administration "tends to look at intelligence officers, law enforcement, judiciary and assume they're part of the partisan process and treat them as such," Sipher said.

"However, the people who work — professional intelligence officers, FBI officers — have been working for a number of administrations. They are nonpartisan and will follow the information where it goes. I think this will continue. I think our institutions are stronger than this."

On Tuesday, White House spokesman Sean Spicer said Trump fired Comey "based on the clear recommendations of both Deputy Attorney General Rod Rosenstein and Attorney General Jeff Sessions."

Rosenstein focused on Comey's statements days before the November election about the FBI investigation of Hillary Clinton's email practices. During the final days of the campaign, Trump had praised Comey's announcement, which Clinton blames for her loss to Trump.

In a letter to Comey, Trump said the firing was necessary to restore "public trust and confidence" in the FBI.

Comey's abrupt dismissal came amid the FBI's investigation into Russia's influence on the 2016 U.S. election, including possible links between Moscow and Trump campaign officials. Comey confirmed the probe in March.

Some Republicans said Comey's firing will be a fresh start, while others called Trump's dismissal bad timing.

Many Democrats called for Comey to immediately be summoned to testify to Congress about the status of the Trump-Russia investigation. Senate Minority Leader Charles Schumer said the Justice Department should appoint an independent prosecutor for the Russia inquiry.

In a tweet on Tuesday night, Trump took aim at Schumer.

@realDonaldTrump: Cryin' Chuck Schumer stated recently, "I do not have confidence in him (James Comey) any longer." Then acts so indignant. #draintheswamp

On Wednesday, Trump continued to tweet on Comey's firing.

@realDonaldTrump: The Democrats have said some of the worst things about James Comey, including the fact that he should be fired, but now they play so sad!

James Comey will be replaced by someone who will do a far better job, bringing back the spirit and prestige of the FBI.

Comey lost the confidence of almost everyone in Washington, Republican and Democrat alike. When things calm down, they will be thanking me!

—The Associated Press and CNBC's Christine Wang contributed to this report.