May's Conservative Party has long criticised the Strasbourg-based European Court of Human Rights (ECHR), which enforces the convention, as an encroachment on British sovereignty.
But supporters of the convention say it is an important safeguard of human rights in Britain, which does not have a written constitution enshrining fundamental rights.
In a speech to a pro-Conservative political conference, May said that ahead of the next general election in 2015 her party should commit to tackling the issue.
"By 2015 we'll need a plan for dealing with the European Court of Human Rights. And yes, I want to be clear that all options - including leaving the convention altogether - should be on the table," May said.
This view had been floated in newspapers a week ago but it was the first time May had spoken out in person so explicitly. She has been accused of spearheading a Conservative "lurch to the right" following a humiliating defeat in a parliamentary by-election on March 1, when the party was beaten into third by the anti-Europe UKIP.
The ECHR is not an institution of the European Union, but it has become wrapped into a wider debate about Britain's ties with the EU. Prime Minister David Cameron, the Conservative leader, has pledged that if his party wins the 2015 election, a referendum will be held by 2017 on whether to stay in or leave.
By coincidence, May was speaking on a day when radical Muslim cleric Abu Qatada, whose case is the example most often cited by British critics of the ECHR, was sent back to jail for breaching his bail terms.
The government wants to deport the cleric to Jordan, where he is wanted on terrorism charges, but the ECHR ruled in January last year that he could not lawfully be deported because a trial in Jordan could be tainted by evidence obtained under torture.
'Moving the goalposts'
The ECHR overruled Britain's top court on the issue, causing a furore in Britain. Many critics say decisions like the Qatada judgment protect the human rights of those who show little regard for the human rights of others.
"When Strasbourg constantly moves the goalposts and prevents the deportation of dangerous men like Abu Qatada ... we have to ask ourselves, to what end are we signatories to the convention?" May said in her speech on Saturday.
"Are we really limiting human rights abuses in other countries? I'm sceptical. But are we restricting our ability to act in the national interest? Are we conceding that our own Supreme Court is not supreme? I believe we are."
Scrapping the European Convention on Human Rights would be a controversial step and may not be easy.
The Conservatives had pledged in their campaign manifesto for the 2010 general election that they would replace the Human Rights Act, the legislation that enshrines the European convention in British law, with a new British bill of rights.
The government, a coalition of Conservatives and Liberal Democrats, set up a commission of experts in March 2011 to investigate how to create a bill of rights. The commission reported in December 2012 that its members had failed to reach agreement on what should be done.
The British press writes that Theresa May is likely to be the next Tory leader if David Cameron loses the next general election.
