Oxfordshire County Council leader Ian Hudspeth has said he would oppose a new bridge over the Thames near Reading.
Calls for the new bridge, linking the A329 with Caversham, were revived after flooding shut Sonning bridge earlier this month, causing traffic congestion.
Conservative councillor Mr Hudspeth said: “In principle, Oxfordshire County Council is opposed to an additional bridge across the Thames.
“The concerns are if there is a third bridge it may deliver additional traffic impact on South Oxfordshire.
“We want to make sure there would be sufficient mitigation in place so we were not making South Oxfordshire a major rat-run."