May said Britain could leave the ECHR if British courts were not allowed to overrule the decisions of the Strasbourg court, which ultimately decides ECHR cases.
But supporters of Britain leaving the EU claim that such a position is unlikely to be compatible with membership of the ECHR, which is based upon the court being the ultimate arbiter.
In a speech, May, who advocates staying in the EU, said, "The case for remaining a signatory of the European convention on human rights, which means Britain is subject to the European court is not clear.
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"Because, despite what people sometimes think, it was not the EU that delayed for years the extradition of Abu Hamza, almost stopped the deportation of Abu Qatada and tried to tell Parliament that however we voted, we could not deprive prisoners of the vote. It is the European convention on human rights."
May, seen by some as a potential Tory leader if David Cameron loses the 23 June referendum, said, "The ECHR can bind the hands of Parliament, adds nothing to our prosperity, makes us less secure by preventing the deportation of dangerous foreign nationals and does nothing to change the attitudes of governments like Russia's when it comes to human rights.
"So, regardless of the EU referendum, my view is this: if we want to reform human rights laws in this country, it isn't the EU we should leave, but the ECHR and the jurisdiction of its court."
May's call for a British bill of human rights is squarely in line with Conservative party policy, but in calling for Britain to leave the European convention on human rights, she is going beyond what the government proposes.
Responding to her speech, UKIP justice and home affairs spokeswoman Diane James said, "May is pulling out this tattered rag of an argument to comfort disgruntled Tories without checking the facts."
The MEP added, "The facts are that by EU treaty law we must be signatories of the European Convention of Human Rights and the UK is bound by its judgements. To say otherwise is misleading people or at best not to be aware of the legal truth.
"The Home Secretary is now drowning in a sea of fact. One day she acknowledges that it is more difficult to control immigration while we are members of the EU.
"Another day she raises the issue of the ECHR, saying we must leave it, but fails to tell people we can only leave it if we first leave the EU."
James added, "There is no escape from EU control of our human rights legislation, or from domination of our law by the ECHR, as long as we remain members of the EU."
In April 2011, the European Commission, in response to UKIP leader Nigel Farage, said that "respect for fundamental rights as guaranteed by the European Convention on Human Rights is an explicit obligation for the Union under article 6(3) of the treaty on European Union.
"The rights secured by the convention are among the rights guaranteed by the Charter of Fundamental Rights of the EU which are likewise addressed to member states when they implement Union law. In the negotiations for the accession of new Union members, respect for the convention and the case law of the European Court of Human Rights is treated as part of the Union acquis."