Vice President-elect Mike Pence received a surprise dinner invitation on Monday night from his new neighbors in leafy northwest Washington. They asked him to dine with them at Comet Ping Pong, the pizzeria at the center of debate over whether allies of President-elect Donald J. Trump are spreading so-called fake news.

In an open letter posted on the online blogging platform Medium, Mr. Pence’s neighbors — part of a coalition that describes itself as opposed to the “unacceptable practices and policies in the Trump administration” — implored the vice president-elect to “help bring an end to this madness through the simple act of breaking bread.” There was no immediate comment from Mr. Pence or a spokesman.

During the transition period, Mr. Pence and his family have rented a temporary home in a heavily Democratic area not far from Comet Ping Pong, a popular dining spot for families with children. The restaurant became caught up in a bizarre conspiracy theory after fake news reports claimed the pizzeria was operating a child sex slave ring linked to Hillary Clinton.

Earlier this month, that fake story led to the firing of real bullets, when a gunman showed up at Comet Ping Pong, saying he had come to “self-investigate” the claims, and fired shots inside, terrifying the entire neighborhood. No one was injured, and the police arrested Edgar M. Welch of Salisbury, N.C., who remains in jail. The episode drew new attention to the Twitter habits of Lt. Gen. Michael T. Flynn, Mr. Trump’s pick for national security adviser, who has used social media to spread fake news stories.