Michael Gove has pointedly declined to deny a report that Liz Truss’s personal phone was potentially hacked by Russian agents, as Labour accused the government of “not taking national security seriously enough”. Gove, returned to the cabinet this week by Rishi Sunak as levelling up secretary, said he could not discuss any possible security breaches, while insisting there were “robust protocols” in place over such issues. The Mail on Sunday said the agents who had hacked into Truss’s personal phone when she was foreign secretary were believed to have gained access to secret exchanges with other nations, as well as private chats with Kwasi Kwarteng, who was later her chancellor when she was in No 10. Asked about the claims, Gove told Sky News’s Sophy Ridge on Sunday programme: “I don’t know the full details of what security breach, if any, took place. What I do know is that the government has very robust protocols in place in order to make sure that individuals are protected, but also that government security and national security are protected as well.” Asked about reports that the incident had been covered up by Simon Case, the cabinet secretary, with Truss in part worried the revelation could harm her bid to succeed Boris Johnson, Gove said: “I’m sure that Liz both as foreign secretary and as prime minister will have followed the advice that she was given by the intelligence and security communities.” Speaking after Gove, the shadow home secretary, Yvette Cooper, said the return of Suella Braverman as home secretary by Sunak, only six days after Truss sacked her for security breaches, highlighted a wider lack of seriousness over security. “All of these just raise questions about the way in which the government is not taking national security seriously enough,” Cooper told the Ridge show. “The problem is that the person who should be providing reassurance that the government has a grip, the person who ought to be doing interviews this morning about all of this, is the home secretary, Suella Braverman, and she can’t do that because she’s still unable to answer questions about her own serious security breaches and lapses.” Braverman was dismissed by Truss after it emerged the then-home secretary had been using a personal email to send sensitive government information on immigration policy to a Tory MP. She accidentally copied the message to another MP’s aide, who alerted No 10. Cooper said Labour wanted answers over whether Braverman was involved in any earlier security breaches, and wanted any information uncovered by Case and the Cabinet Office more widely to be sent to parliament’s intelligence and security committee, which oversees security issues. “We’ve been asking repeatedly whether the home secretary has used her personal phone to send other government documents,” Cooper said. “There’s also questions about whether she was investigated or other security leaks. “This is just irresponsible. You can’t have a home secretary who is not trusted by the Security Service, who is not trusted with important government information.” Quizzed about Braverman, Gove said the home secretary was “a first-rate, front-rank politician”. He said: “She acknowledged that a mistake had been made. She is working hard in order to ensure that our borders can be made more secure, and that policing is more effective. She’s a valued member of the cabinet and someone whom I admire and like.” In a later interview with BBC One’s Sunday with Laura Kuenssberg show, Gove appeared to blame the media in part for overly focusing on the issue of Braverman’s security breach, and said the very fact she had been returned to government should be enough reassurance for people. While saying he did not wish to criticise journalists, Gove said “it becomes a distraction if people are asking these questions”. Asked how people could be sure she was not compromised by her approach to the role, Gove added: “By definition, Suella coming back into office is a sign of confidence on the part of the government as a whole that she is equipped, ready and more than able to deal with the task in front of her.”