The D.C. government employee who complained to the news media that he did not have enough work assigned to him was assured yesterday by Mayor Sharon Pratt Dixon that within a few days he would have "challenging work" to do.

Carl R. Greene, a computer expert, met with Dixon at her request. After the 30-minute meeting, Greene said he believed Dixon was sincere in her campaign promises to make the government more efficient.

"I am a taxpayer and I care about this city," Greene said. "I will do my part to help with the deficit."

Greene was assured in advance that he would not be fired for speaking out about his dissatisfaction with the finance office, where he is paid $47,000 and has done almost no work for seven months.

Dixon told reporters that she felt Greene has done work during the past seven months but that he has not been challenged in his job.

Dixon said she will make it clear to managers, including Greene's supervisor in the Office of Financial Management, that they are to make sure all workers are challenged.

"We don't want our employees to be sluggish," she said. "We don't want our employees to feel less than enthusiastic about coming to work. We want them to get to work on time, if not early. We want them to render quality service."

Dixon said she would establish an ombudsman office for employees like Greene to make their complaints known.

Greene, 33, an accountant, complained to reporters this week that he has been given little to do since he was transferred to the financial management office from the public housing agency last July.

He said his usual workday, until yesterday, consisted of long coffee and lunch breaks and a workout at his health club.

Greene said his phone rang all day yesterday as colleagues called to praise him for his courage in speaking out while others told him they were in the same situation. He received an invitation to interview for a job at the federal Department of Housing and Urban Development.

Greene, who was hired by the city in 1982, was credited with saving the taxpayers an estimated $370,000 in 1989 when he created an accounting system for the 12,000 tenants who live in public housing and computerized the records for the Tenants Assistance Program. His work at the public housing agency was recognized with a plaque and an incentive award of $800.

Since then, he said, he has been passed over for promotion. Although his expertise is in computer systems, he was given an office with no computer when he was transferred to his current job.

Valerie Holt, his supervisor until recently, said Greene had been given ample work to do and had completed it satisfactorily.

Greene said he expects to be at his desk today and tomorrow, but again he doesn't expect to have any work to do.

"I haven't heard from my supervisor," he said. "As far as I know, I still have nothing to do."