The FSA is planning to force insurers to deal with claims within a specific time frame.
The plan already applies to life insurers.
FSA managing director John Tiner said there is "evidence" that insurers' claims records are poor. "We are looking at imposing rules to ensure standards get better, he said."
But an ABI spokesman said: "It is important that any new rules benefit the consumer and are proportionate."
The FSA hopes the changes will simplify regulation, because insurers will no longer have to deal with both the ABI and GISC. However, analysts fear penalties will be harsher as a result.