The chief executive of America's National Public Radio (NPR) network has quit her post after a video sting by rightwing activists posing as campaigners for a fictitious Muslim group.

Vivian Schiller resigned as NPR chief executive a day after the release of a video of a lunch at a fashionable Georgetown restaurant in which fundraisers for the network and the imposters discussed racist tendencies in the Tea Party, as well as the anti-intellectual streak in Republicans, Jewish media "conspiracy", and a potential $5m donation to public broadcasting.

The undercover operation was engineered by the conservative activist James O'Keefe, who made his name with a previous undercover sting against Acorn, a community organisation much reviled by the right in the US.

The senior NPR fundraiser in the video, Ron Schiller, who is no relation to the former chief executive, had been due to leave the radio network for the Aspen Institute.

But Schiller told reporters on Wednesday he would not be taking that job.

In the 11-minute, heavily edited video, he denounces the Tea Party as scary, seriously racist, and weirdly evangelical. "I mean basically they are, they believe in sort of white, middle-America, gun-toting. I mean, it's scary. They're seriously racist, racist people."

In the video Schiller offers no reaction to the impostors' claims to be a front group for the Muslim Brotherhood and laughs when one of the men jokes that NPR should be known as National Palestinian Radio.

Vivian Schiller immediately condemned his "appalling" comments, and the network made clear that it had never intended to accept the proffered $5m.

But in a conference call with reporters, Dave Edwards, the chairman of the NPR board, said that Schiller had to go. "The CEO of any organisation is accountable for all of the operations of that organisation," he said.

Vivian Schiller's exit is the latest in a string of high-profile and speedy departures from NPR since last autumn.

The episode led to immediate calls from Republicans to cut off funds to public broadcasting, and columnists predicted further turmoil for NPR.

The media commentator Jeff Jarvis said on his blog that Schiller's departure suggested NPR's board was too weak in the face of political pressure. Others suggested that NPR had been too quick to "sack" its chief executive.

The network acknowledged some of the turmoil hitting the organisation. "I recognise the magnitude of this news – and that it comes on top of what has been a traumatic period for NPR and the larger public radio community," Edwards said in a statement.

NPR had yet to fully recover from its clumsy sacking of Juan Williams, a political analyst who did double duty on the rightwing TV network Fox News. Williams, who had been at NPR for 10 years, was sacked for comments made on Fox last October when he said that he felt nervous getting on a plane with people dressed in "Muslim garb".

The sacking, and a network official's snide comments about Williams's mental state, made the commentator a hero to conservatives, who embraced him as a victim of political correctness.

Williams also got a full-time job with Fox. Three months later NPR forced out the news executive who had sacked Williams.

But Williams's dismissal had already inspired O'Keefe, who arranged for two colleagues to pose as activists for a Muslim Brotherhood front group which was offering NPR $5m with no strings attached.

Potential damage to NPR was compounded by the fundraiser's assertions that the network would be better off without federal funds.

In public, however, NPR executives have been fighting hard to stop Republican cuts to public broadcasting.

The exposé of NPR is the second big coup for O'Keefe, although he also has credibility problems. He came to fame in 2009 with a takedown of Acorn, an organisation that had worked for 40 years with poor communities. In 2009, he and a female accomplice visited Acorn offices posing as a pimp and prostitute seeking advice on evading taxes. Acorn disbanded late last year.

But O'Keefe pleaded guilty last year to bugging the telephones of the Louisiana Democratic senator Mary Landrieu, and was sentenced to three years' probation. He was also caught conspiring to lure a CNN reporter to a houseboat for a sex tryst, which he planned to film with hidden cameras.