The reviews are in for Lester Holt's performance during the presidential debate, and they're mostly positive

After weeks of arguments about the proper role of a presidential debate moderator, Lester Holt's performance during the first presidential debate appeared to go over successfully.

Many observers from various political stripes claimed that the NBC anchor effectively modulated his role, pushing and fact-checking both Donald Trump and Hillary Clinton occasionally, but largely refraining from definitively ruling in favor for either candidate.

"I've been there. I thought Lester Holt did a fine job," Fox News host Megyn Kelly said shortly after the debate concluded.

"Conservatives should agree @LesterHoltNBC did a very fine job moderating. He pushed on birther issue and Iraq war but gave plenty of time," conservative radio Host Hugh Hewitt, a Trump-backer, tweeted.

Others agreed:

The Clinton campaign also appeared pleased with Holt's performance.

"I thought Lester Holt did a good job, I think it was a very informative debate," Clinton campaign manager Robby Mook told reporters.

Asked whether the campaign hoped Holt would fact check more, Mook said the campaign was "happy with the debate as it went."

Trump himself told CNN that he was satisfied with Holt's performance.

"I thought Lester did a great job," Trump said. When asked by CNN whether the questions were fair, the real-estate mogul said he "thought it was great."

But some of Trump's top supporters disagreed.

Former New York Mayor Rudy Giuliani criticized Holt for characterizing the city's former "stop-and-frisk" policy as unconstitutional. A federal judge ruled the way the city practice the tactic as unconstitutional in 2013.

"I think it's outrageous that Lester Holt interfered in a legal discussion he knows nothing about on the side of Hillary Clinton. And I didn't see him once interfere on the side of Donald Trump," Giuliani told reporters. "He should be ashamed of himself."

Breitbart News, a popular far-right organization that has thrown its support behind the real-estate magnate, slammed Holt, publishing articles accusing the anchor of "shilling for Hillary." The Drudge Report, another popular news source for conservatives, called Holt "the third debater."

Trump advisor Sarah Huckabee-Sanders said that the NBC anchor did a good job overall, though she complained that Holt parroted Clinton talking points.

"He had the weight of the world on his shoulders," Huckabee-Sanders said of Holt.

For weeks, observers quarreled over whether the presidential moderators should actively fact-check Trump, who has made a record number of notably false claims, and Clinton, who has made her fair share of untrue statements. Fox News anchor Chris Wallace, who will moderate the final presidential debate, said it was not the moderator's job to be a "truth squad."

Brett LoGiurato and Allan Smith contributed reporting.