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The PM claimed a Labour government would not be "unequivocally committed to the nuclear deterrent".
Shadow defence secretary Nia Griffith rebuked her colleague Emily Thornberry for suggesting Trident could be subject to a review, if Labour won power.
Jeremy Corbyn said Labour's manifesto was "very clear" and the party was committed to Trident's renewal.
But Mrs May said: "They would not be able to defend this country. A Jeremy Corbyn-led Labour government could not be trusted with the defence of our country."
The Conservatives said it showed Labour had a "chaotic and divided team" who would make "a mess ... of our Brexit negotiations".
Labour's manifesto included support for renewing Trident, even though Mr Corbyn is a long-standing opponent of nuclear weapons.
The Commons backed the renewal of Trident in 2016, by 472 votes to 117, approving the manufacture of four replacement submarines. Labour was split over the issue, with 140 of its 230 MPs going against their leader and backing the motion in a free vote.
The issue resurfaced on Friday following an interview with Shadow Foreign Secretary Emily Thornberry on LBC radio, in which she said she was "sceptical" about Trident.
When asked to confirm that it would remain Labour policy after a defence review, she added: "Well no, of course not, if you are going to have a review, you have to have a review."
But shadow defence secretary Nia Griffith told BBC Newsnight: "With all due respect, Emily is not the shadow defence secretary. I am."
She said the party was "fully committed" to having a nuclear deterrent and that the defence review would look at how a Labour government would spend money.
"What it is not about is actually questioning whether we would have a Trident nuclear deterrent because we settled that last year," she added.
Asked if Ms Thornberry was wrong, Ms Griffith went on: "Indeed. Last year we looked at it, in particular, at the national policy forum and it was decided that we would keep the nuclear deterrent."
BBC political correspondent Mark Lobel said Ms Thornberry's team had since said there was no difference between the two shadow ministers in terms of party policy and she had been expressing her personal view about Trident's viability and costs.
Mr Corbyn, campaigning in Birmingham ahead of the 8 June election, told reporters: "The manifesto makes it very clear that the Labour Party has come to a decision and is committed to Trident.
"We're also going to look at the real security needs of this country on other areas such as cyber security, which I think the attack on our NHS last week proved there needs to be some serious re-examination of our defences against those kind of attacks."
Pressed again, he said: "I've just made it clear and included in our manifesto is an absolute commitment which is given by party and which is given by me that we will also pursue multilateral disarmament through the nuclear non-proliferation treaty, and that is a position that has been held for a long time by the party."
Labour's backing for Trident was agreed by a vote at its party conference but Mr Corbyn has previously suggested the party would carry out a strategic defence review if it won power and that Trident would be part of that.