In her message, Ms Mowlam, who was moved into the Cabinet Office from Northern Ireland by Tony Blair last month, blamed a recent bout of flu for having been below par.
The Prime Minister's official spokesman also acted quickly to scotch the rumours as untrue. "I know Mo had flu and was feeling a tad under the weather. How this gets translated into `I hate my job' I don't know."
There had been rumours circulating in Westminster for weeks that Ms Mowlam was unhappy with her new job after privately wanting a big portfolio with a budget.
But the last straw for her was a front-page report in The Daily Mirror saying she had told friends she hated the "meaningless" role she had been given. She felt the move by Mr Blair was a "stitch-up" that had stalled her career, the report said.
At Whitehall yesterday, she told staff: "Some of you may have noticed a story in The Mirror today suggesting that I am unhappy with my job here at the Cabinet Office. In case you are concerned that this might affect how I do my job, I would like to say that nothing could be further from the truth."
She said leaving Northern Ireland after a number of years was difficult. "I lived and worked there, so my sadness was as much about leaving a place and people I had got to know well as leaving the job.
"But having been round most of the department here now, met many of you and discussed some of the many important issues we deal with, I am certainly looking forward to working together with you to meet all the challenges that face us."
She added: "I have had a bit of flu recently and that's laid me low but as those of you know who have been working with me closely, it certainly hasn't stopped me. I just wanted to let you know that my commitment to the work we have to do here together is 100 per cent. And no amount of nonsense in the press will deflect me from that."
She privately recognises that the letter - e-mailed to all staff and copied on paper to them - will not be enough by itself to scotch the rumours.
In July there were strong rumours that Mr Blair had promised to appoint her as Secretary of State for Health to replace Frank Dobson, when he stepped down to run as Labour's candidate for the mayor of London.
Ministers privately said that Mr Dobson had gone "ballistic" when he heard that Ms Mowlam had been offered his job and refused to move.
After delaying the Cabinet reshuffle, Mr Blair put Alan Milburn into the health post and gave Ms Mowlam the role in the Cabinet Office previously occupied by two Cabinet `failures' - David Clark and Jack Cunningham.
There were suggestions that, having failed to land a Cabinet job with a big budget in Whitehall, Ms Mowlam was sulking.