The decision by May means the story is likely to stay on the agenda as most written questions to government departments should be answered within one working week.
A Conservative spokeswoman said: 'There are still a number of issues left unanswered.'
The decision will come as a blow to the DTLR, which this week sought to bring an end to the PR blunders that have plagued the department since its creation last year.
A statement issued on Tuesday by the DTLR said: 'Both the department and Martin Sixsmith have agreed that this brings the matter to an end and that no further comment should be made.'
The statement added that the DTLR had been wrong to announce that Sixsmith had resigned in February and that his contract will now officially end this month by 'mutual agreement'.
The Prime Minister's official spokesman has also sought to end media interest. At Tuesday's lobby briefing he dismissed the events surrounding Sixsmith's resignation as, 'an incorrect understanding' that had occurred 'in good faith.' He refused to answer questions relating to a payout to Sixsmith, despite media speculation putting the figure at around £200,000.
Sixsmith's role is being filled on an interim basis by DTLR head of marketing and corporate communication Charles Skinner.