Mr. Giuliani could not immediately be reached on Sunday for comment.

Mr. Giuliani has been a ubiquitous presence on television news in recent days, advocating on Mr. Trump’s behalf. He has repeatedly alleged that Mr. Biden, while serving as vice president, intervened in Ukraine to assist his son Hunter Biden’s business interests. No evidence has surfaced that Mr. Biden intentionally tried to help his son in Ukraine.

The Biden campaign argued that Mr. Giuliani’s television appearances had allowed him to mislead the viewing public — and suggested that network journalists had done too little to hold him to account. “While you often fact check his statements in real time during your discussions, that is no longer enough,” the letter said.

Mr. Biden’s advisers have not been shy about offering advice to journalists . Earlier this month, the campaign sent a memo to an elite group of campaign reporters warning that any news story would be “misleading” if the Trump camp’s claims about Mr. Biden were unsubstantiated.

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The news networks had no comment on Sunday.

As Mr. Trump’s personal lawyer, Mr. Giuliani remains a highly newsworthy figure, particularly amid an escalating impeachment inquiry in which Mr. Giuliani’s own actions in Ukraine could play a central role. It is likely that Mr. Giuliani will remain a coveted booking for television journalists seeking insight into the president’s mind-set and legal defense strategy.

As for Mr. Biden, he has shown little eagerness to engage one-on-one with TV anchors. The former vice president has declined to appear on any of the weekend political talk shows since declaring his candidacy, reserving his on-air appearances for late-night comedy shows, “The View” and a small number of other sit-downs.