President Trump has ratcheted up his criticism of special counsel Robert S. Mueller III's investigation into Russian interference in the 2016 election, calling out Mueller by name for the first time and asking if anyone thinks the investigation is fair given that the investigative team includes “13 hardened Democrats” and “Zero Republicans” — despite Mueller himself being a registered Republican.

But that's not how most Americans view things. Mueller is largely seen as running a fair investigation, and confidence has held steady or even grown over recent months, despite increasing scrutiny from Republicans and Trump of the investigation.

A Pew Research Center poll released last week found that 61 percent of Americans are very or somewhat confident that Mueller “will conduct a fair investigation,” up six percentage points from 55 percent who said the same in January, and from 56 percent in December. The rise is modest but statistically significant, and it comes after the release of a Republican memo in early February accusing senior law enforcement officials of misleading a court to conduct surveillance on a former Trump campaign adviser.

Democrats and Democratic-leaning independents fueled the rise in support for Mueller in the Pew survey, with 75 percent saying they are at least somewhat confident he will conduct a fair investigation, up from 65 percent in January. Just under half of Republicans, 46 percent, express confidence in Mueller's probe this month, hardly changed from 45 percent two months ago.

Other polls show that Americans' confidence in Mueller has been steady or increasing slightly in the past couple of months, though the overall level of support for his probe has varied across polls asking different specific questions.

In February, a Marist poll found that over half of Americans, 53 percent, considered Mueller's investigation to be fair, while 28 percent said it was not fair, and 20 percent had no opinion. That compares with a 48 percent-28 percent fair-not fair margin in January.

Also in February, a CNN-SSRS poll found 47 percent of Americans approving of the way Mueller was handling the investigation while 33 percent disapproved, both nearly identical to similar surveys in January and December.

Public confidence in Mueller may have declined from an earlier high point in the fall. A January Washington Post-ABC News poll found 50 percent of Americans approving of the special counsel's handling of the investigation, down eight points from a Post-ABC poll in early November.

The Marist poll found 77 percent of Democrats and 51 percent of independents saying the investigation was fair, up marginally from January; 35 percent of Republicans said it was fair, while 46 percent said it was unfair.

Mueller's durable reputation this year sheds some light on how Americans could feel about Trump's potential efforts to remove the general counsel, a move that the president sought in the summer and that gained fresh relevance this weekend with Trump's first direct criticism of Mueller.

On CNN's “State of the Union” on Sunday, Sen. Lindsey O. Graham (R-S.C.) warned that if Trump were to order the firing of Mueller, “that would be the beginning of the end of his presidency because we're a rule-of-law nation.”

The February Marist poll found overwhelming opposition to such an action. A 70 percent majority of Americans said Mueller should be allowed to finish the investigation, while 16 percent said he should be fired. Republicans, who largely approve of Trump's performance, opposed firing Mueller by roughly 2 to 1, 55 percent to 27 percent.

Scott Clement contributed to this report.