The defence secretary has repeatedly refused to confirm details of the missile test that reportedly failed.
Michael Fallon cut short a regional visit to be summoned to the Commons to answer questions today.
Mr Fallon would not give any details on the test, citing national security, but reiterated many times: "HMS Vengeance is successfully certified and has passed the test that was set."
There are very few things that we cannot discuss openly in parliament but security of our nuclear deterrent is certainly one of them.
Mr Fallon said he "disagrees with greater call for transparency" and it "has never been practice to give parliament details of the demonstration and shakedown of operations".
As Mr Fallon was speaking, CNN reported an unnamed US defence official with direct knowledge of the incident had confirmed the unarmed Trident II D5 missile veered off course after being launched from a Royal Navy submarine off the coast of Florida.
The US official was reported to have said the altered trajectory was part of an automatic self-destruct sequence triggered when missile electronics detect an anomaly.
The reports have led to claims of a "cover-up", as MPs were not told about the June 2016 test when they voted on the £40 billion renewal of the Trident system the following month.
Mrs May confirmed she was informed about the test before addressing MPs ahead of the vote, which came just days after she entered office.
Speaking after a Cabinet awayday in Cheshire, Mrs May said: "I'm regularly briefed on national security issues, I was briefed on successful certification of HMS Vengeance and her crew.
"We don't comment on operational details for national security reasons."
She added: "The key issue about the debate we had in the House of Commons on the future of Trident, is whether we should renew Trident for the future.
"Should we continue to have an independent nuclear deterrent?
"I have absolute faith in our independent nuclear deterrent."