“This is going to be a hard-fought, heated campaign of ideas,” the anchor added. “In the days and weeks and months ahead, I will strive to do a better job myself of elevating the political discussion.” Mr. Matthews concluded by congratulating Mr. Sanders on his Nevada victory.

MSNBC’s commentators are influential with the Democratic base, and they convey a variety of left-leaning views. Their mixed opinions about Mr. Sanders have mirrored some of the divisions within the party itself as he has jumped to the lead of the nominating race.

Perhaps because of the channel’s popularity with Democrats, Mr. Sanders’s campaign has singled out MSNBC for criticism, complaining about Mr. Matthews and the political anchor Chuck Todd, who recently read on his program a column by a conservative writer that referred to Mr. Sanders’s aggressive online supporters as “brownshirts.”

The New York Post reported that Mr. Sanders had personally complained to MSNBC and NBC News executives about the network’s coverage during a debate walk-through last week in Las Vegas.

Mr. Matthews’s World War II comments, however, drew condemnation beyond the Sanders inner circle, including from the MSNBC contributor Anand Giridharadas.

“Many in this establishment are behaving, in my view, as they face the prospect of a Bernie Sanders nomination, like out-of-touch aristocrats in a dying aristocracy,” Mr. Giridharadas said on MSNBC on Sunday morning. He added, “Why is Chris Matthews on this air talking about the victory of Bernie Sanders, who had kin murdered in the Holocaust, analogizing it to the Nazi conquest of France?”