Speaking to a British parliamentary committee, Natacha Bouchart also said it was easier to get welfare benefits in Britain and that migrants viewed the country as an "Eldorado".
"I think the border should be on British territory because it's up to you to decide the migrants you want to let in or not," said the mayor, from the opposition centre-right UMP party.
She called for "joint measures on both sides to better regulate the flow and give serenity to the local populations in and around Dover and in and around Calais".
Up to 2,300 migrants are thought to be in Calais and surrounding areas, overwhelming security forces as they make regular attempts to mob the port en masse to try and scramble onto trucks boarding ferries to the British port of Dover.
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"You have to put the message across that there is no point going to Calais to get into Britain because Britain is no longer taking in migrants," she said.
The problem in Calais is not new, illegal camps of migrants have sprung up in the area ever since French authorities closed down the infamous Sangatte immigrant detention centre in 2002.
This former hangar run by the French Red Cross used to be home to a perpetually renewing population of migrants, many of them Afghans and Iraqi Kurds who hoped to sneak through the under-sea Channel Tunnel to Britain.
Authorities have announced they will open a day facility to allow migrants access to health care, toilets and bathrooms, but appear to have so far ruled out any permanent 24-hour centre.