Councils can still apply to run their own local scrappage schemes using cash from the Government's £220 million Clean Air Fund, the Department for Environment, Food and Rural Affairs (Defra) said.
The prospect of offering diesel drivers compensation to scrap or modify high-polluting vehicles was raised last year as a potential measure to tackle air pollution.
Also in the news: Are modern vehicle headlights too dazzling for drivers?In a formal response to a consultation published on Friday, the Government said: "A targeted scheme would be difficult to deliver, potentially open to abuse and could disrupt the existing car market."
"In response to these concerns we are not proposing to take forward a national scrappage scheme at this time."
The move has angered campaigners, including Morten Thaysen, from Greenpeace UK.
"The government has just performed a tyre-burning U-turn on the national scrappage scheme," he said.
"This measure would have been a good opportunity to take polluting cars off our roads while helping drivers who bought dirty diesels on a false prospectus.
"Instead, ministers are once again passing the buck to local authorities."
Diesel tax, benefits and five other law changes you need to know about in 2018But Defra denied performing a U-turn.
A spokeswoman said: "It is wrong to claim that we have changed our position or ruled out scrappage. We have consistently said that any potential scrappage scheme would be targeted.
"Today's announcement confirms this position, making it clear that councils with poor air quality can put forward plans for local scrappage schemes under the Clean Air Fund."