Defence Secretary Michael Fallon stressed her track record as Home Secretary, chairing the Whitehall Cobra emergency committee and being a member of the National Security Council.
Asked if there would be risks if her leadership rival Andrea Leadsom became Prime Minister – rather than Mrs May, he told BBC radio: “I’m not going to knock her opponent but I’m committed to Theresa May, I’ve worked with her on security day in, day out.
“She has the experience…and I’ve seen her deal with crisis, I’ve seen her chair the Cobra emergency committee, I’ve seen her handle these things, and she’s absolutely committed above all to keeping this country safe.”
In a sign of the support from Cabinet ministers and other senior Tories behind Mrs May, former party chairman Sir Eric Pickles also tweeted: “I will be voting for Theresa.
“We will all be safer with this sensible, trustworthy and totally decent person in Downing Street.”
But Cleethorpes MP Martin Vickers, backing Mrs Leadsom, stressed Mrs May had failed to meet the Government’s flagship goal to cut net migration to below 100,000.
Mrs May’s supporters were also seeking to link Mrs Leadsom with Ukip, after Nigel Farage voiced his support for the latter to become Tory leader.
An MP backing the Home Secretary claimed: “The surge in support that some people talk about for Andrea has a lot to do with people who support Ukip.
“But Conservative party members have a mind of their own.”
Mrs Leadsom swept into the last two leadership contenders, brushing aside a challenge from Justice Secretary Michael Gove, and gaining the backing of 84 MPs to Mrs May’s 199.
But the energy minister, one of the leading figures in the Brexit campaign, has faced a series of searching questions over whether she exaggerated her City career on her CV.
She has also yet to publish her tax return as she pledged to do if she made the last two.
However, her supporters believe that she will appeal to many rank-and-file Conservative members with her views on gay marriage, fox-hunting and business.
Some 150,000 Conservative members will decide the identity of the party’s new leader who will become the country’s second female Prime Minister after Margaret Thatcher.
The result of the contest is due on September 9 after a summer of campaigning by the two candidates.
But a move by former party chairman Grant Shapps to speed up the leadership race so a new PM is chosen by the end of the month was gathering pace and now has the backing of 44 Tories and one Labour MP.
Some MPs and Tory members believe a new premier should be selected as quickly as possible rather than delay matters given the economic and political turmoil gripping Britain.
Long-standing Conservative member Dr Sarah Ingham, former deputy chairman of Chelsea and Fulham Conservative Association, said: “In an ideal world, I would like to see the coronation of Theresa May.”