Mr Campbell says he believes there is little point in the two sides having more exchanges until a parliamentary committee reports back on the issue next week.
His letter comes after a weekend of continued argument, with more ministers entering the row castigating the BBC.
The committee is investigating the BBC's report claiming Downing Street exaggerated an intelligence report issued in the build-up to the Iraq war.
How brave of Mr Campbell to start the war, fire a few salvos from Coward's Castle over the bow at the messenger then run away. Better luck huntin' down and smokin' out the WMDs (Words of Mass Deception) possessed by the BBC.
Alistair old chap have you met my friend Richard?
Alistair old chap have you met my friend Richard?