Sir Keir Starmer has blamed the Tories over previous "failures" following revelations about the secret Afghan data breach.
The Prime Minister said: "There has always been support across this House of the United Kingdom, fulfilling our obligations to Afghans who served alongside British forces.
"We warned in opposition about Conservative management of this policy, and yesterday the Defence Secretary set out the full extent of the failure that we inherited. A major data breach. A super-injunction. A secret route that has already cost hundreds of millions of pounds.
"Ministers who served under the party opposite have serious questions to answer about how this was ever allowed to happen."
PA | The Prime Minister blamed the Tories for previous 'failures'
While Kemi Badenoch opted against talking about the Afghan data breach, Liberal Democrat leader Sir Ed Davey told the Prime Minister that the Liberal Democrats would support efforts to hold a public inquiry.
Davey said: "He [Starmer] will have our support if he decides to pursue a public inquiry."
Downing Street did not rule out a public inquiry into the scheme during a press conference on Wednesday afternoon.
Asked if Starmer would consider holding a public inquiry into the scheme, the Prime Minister's official spokesman said: "We obviously welcome public and parliamentary scrutiny of this issue, of how the decisions that led to this issue came about.
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"For the first time, Parliament is now able to scrutinise this. I think it is right that Parliament is able to scrutinise this issue."
Downing Street added that Starmer was "angry" when he was informed of the breach last summer.
Defence Secretary John Healey was briefed months earlier, while Labour were still in opposition.
No10 rejects the suggestion that Starmer should have been briefed alongside Healey, arguing that it was the Tories who decided who should be told on security grounds.
PA | Former Defence Secretary Sir Ben Wallace defended the Government's decision
Downing Street's press secretary said: "The Prime Minister is angry at such a terrible breach that had such grave consequences being allowed to happen, which is why we've explained that there are questions that need to be answered by Conservative ministers."
The dataset contained personal information of 25,000 Afghans who applied for the Afghan Relocations and Assistance Policy, which was released "in error" in February 2022.
The Conservative Government at the time were granted an injunction to keep the breach secret, while it created a covert relocation scheme to bring in affected Afghan soldiers and their family members to Britain.
Defence Secretary at the time, Sir Ben Wallace, defended the approach taken when the original application was made.
Speaking this morning, Wallace said the Tories needed "time and space" to deal with the situation at the time.