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The E Street Band guitarist and Sopranos actor explained that he had tried to organise a US tour for the band on a number of occasions, the Daily Record reports.
Van Zandt said: "I thought their album before this last one [Riot City Blues] was one of the greatest records in 10 years. I begged them to come over. I had a whole tour for them.
"Their agent talked me out of it. He said: 'They can't do 20 shows'. I'm like, 'Come on, man. We do 20 shows a month'.
The guitarist added: "Primal Scream could be the biggest band in the world. They are fantastic when they make rock records - once every 10 years. But they can't tour because of drug problems, or whatever.
"I don't have patience for it. I'm like, all right, you want to be a drug addict, go be a drug addict. Don't waste my time."
Van Zandt was speaking at the South by Southwest festival in Austin, Texas, a few hours before Primal Scream performed at the event.
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