FSA regulation of travel agents selling insurance would be too burdensome, according to the ABI.
The trade body laid out its proposals for regulation of the sector, in its response to the review by the Treasury of travel insurance.
It proposes that:
The Financial Ombudsman Service is extended to cover customer disputes arising from travel insurance sold as part of travel package arrangements.
Local authority trading standards regulate the selling of travel insurance sold through tour operators and travel agents, similar to the way they monitor extended warranty sales.
There should be an industry code of practice to ensure best practice.
Jane Milne, the ABI's head of property and travel insurance, said: "The UK travel insurance market is highly competitive. There is only a low risk of customers getting the wrong deal.
"Full FSA regulation could burden many agents and operators, leading to less choice and more people travelling without insurance. Our proposals will ensure that everyone buying travel insurance enjoys the proper level of protection, while also maintaining a thriving market."