Ms Huckabee Sanders also rejected calls to appoint a special prosecutor to the FBI investigation into Russia's alleged interference in the 2016 election.
"We don't think it's necessary," she said. "No one wants this to be finished and completed more than us."
Her comments came as the US Senate Intelligence Committee invited Mr Comey to testify before the panel on Tuesday.
Top Democrat Senator Mark Warner said the panel had so far "not heard back".
Washington is still shaking from the aftershocks of Mr Comey's unexpected dismissal.
The move "raises profound questions about whether the White House is brazenly interfering in a criminal matter," said Adam Schiff, the highest-ranked Democrat on the House Intelligence Committee.
But the president stood by his actions on Wednesday during a surprise meeting with Henry Kissinger, saying Mr Comey was fired "because he was not doing a good job".
His first in-person explanation for his actions came before a meeting with Russian Foreign Minister Sergei Lavrov and Russian Ambassador to the US Sergei Kislyak - his first with any Russian official since taking power.
It is only the second time the head of the FBI has been fired.
'Not good optics' - Analysis: Anthony Zurcher, BBC News, Washington
If Donald Trump is trying to avoid comparisons with Richard Nixon's scandal-plagued presidency, welcoming Henry Kissinger - the man probably most closely connected with the former president - in the Oval Office probably isn't the best move.
The whole group meeting with Russian Ambassador Sergey Kislyak was a bit strange, starting with the fact that it happened at all. Given the allegations that Mr Trump fired James Comey because of the FBI investigation into Russia ties to the Trump campaign, meeting with a Russian ambassador the very next day isn't exactly good optics, as they say.
Neither is keeping US media out of the room and having Russian state photographers provide the only public images of the event - images that are sure to be featured in Democratic campaign adverts in the not-too-distant future.
During the campaign, Mr Trump famously joked that he could shoot somebody, and his supporters would stick by him. Smiling with the Russian ambassador in the midst of a growing Russian hacking controversy is the diplomatic equivalent - a brazen move sans firearms.
Many in Washington will howl, but there's no guarantee it will move the needle among the president's legions.