Mr Keymer said Sir Jeremy's partisan speech at the Labour spring conference (LGC, 24 February) could damage cross-party unity in the association.
He added: 'The title of the press release [for the speech] suggests that it is the chairman of the LGA who is attacking the second largest party on the LGA.
'Bearing in mind the large number of Conservative controlled councils and the size of the subscriptions they pay, this is clearly not a very sensible way of keeping the LGA together.'
Sir Jeremy rejected the criticism: 'I was attacking Conservative policy on local government which I'm perfectly entitled to do. I'm also critical of some government policies and I think it would be better for the LGA if the Conservative group would take a different line from Conservative Central Office.'
In an oblique reference to the continuing power of former Tory group leader Lord Hanningfield, Sir Jeremy added: 'For that matter, at least it's clear who the leader of the Labour group is.'