"I understand there are a number of issues that have been raised around the statue," the Conservative leader told the BBC on Friday.
"There should be no suggestion that the threat of vandalism should stop a statue of Margaret Thatcher from being put up," said May, who has dismissed parallels with her fearsome predecessor.
The plan is to put up the 300,000 pounds (339,000 euros, USD 388,0000) bronze statue on Parliament Square next to political greats such as wartime prime minister Winston Churchill and Indian independence icon Mahatma Gandhi.
In 2002, a protester decapitated an Italian marble statue of Thatcher in London's Guildhall Library.
More From This Section
Following her death, graffiti went up around London including one mural reading "Burn in Hell Maggie".
Responding to a planning application for Thatcher's statue to be put up in Parliament Square, a conservation group said a principle of leaving a 10-year gap between the death of a subject and the installation of a statue should be adhered to.
"While Lady Thatcher was also widely respected it cannot be said that she was uncontroversial in this country," The Thorney Island Society said.
The Royal Parks organisation, which manages the land on which the statue would be installed, also objected saying it was not sure Thatcher's family approved.
"Numerous times we have requested assurances from the applicant that they have approval from the family for the statue. To date we have not had those assurances," the Royal Parks said in a letter.
Ivan Saxton, the co-founder of the Public Memorials Appeal Trust which raised funds for the statue, last year said that Thatcher's daughter Carol was opposed to because "there's no handbag".
Her programme of privatisations and deregulation helped turn around Britain's ailing economy and she is also credited with playing a leading role in ending the Cold War.
But she remains a divisive figure, particularly in Britain's working-class heartlands, which suffered devastating industrial decline as a result of the economic rebalancing.
A bronze sculpture of Thatcher was unveiled inside the Houses of Parliament in 2007.