NEW YORK — The Fashion Center Business Improvement District wants to work weekends.

Recognizing the increasingly frantic pace of the garment industry, the FCBID is putting in for a budget increase, in an effort to start offering its security and sanitation services on Saturdays and Sundays.

Barbara Randall, executive director of the not-for-profit organization, said she sent a letter to Mayor Michael Bloomberg on Wednesday, his second day on the job, asking for permission to raise the group’s budget by $1 million — a 33 percent hike.

“We would like to go to seven-day-a-week sanitation and security,” she explained. “A lot of the folks that are moving into the district work less-conventional hours. It used to be this neighborhood just closed down on the weekends, but no more.”

That would mark the first increase to the FCBID’s budget — and the levy charged to landlords in the neighborhood bounded by Fifth and Ninth Avenues and West 35th to 41st Streets — in its eight-year history. During this time, the FCBID has also initiated programs such as signage and lighting improvement in the neighborhood and information services such as a kiosk on Seventh Avenue, a Web site and booklet, as well as creating the the Fashion Walk of Fame.

“It was voted on by the board,” she said. “They actually voted for an increase several years ago, but it was shot down by [former Mayor Rudolph] Giuliani. So on Jan. 2, we wrote to our new mayor to ask for an increase.”

Giuliani had been turning down all requests from BIDs to increase their budgets — which are privately funded but collected by the city and distributed to the organizations — for the last few years of his administration. That has other BIDs, including the Fifth Avenue BID, hoping that the mayor — who has chosen to work in a cubicle and warned most city agencies to prepare for 20 percent budget cuts — will be a little warmer to the BIDs’ cities-help-those-who-help-themselves concept.

Tom Cusick, president of the Fifth Avenue BID, said his group, with heavy retail membership, would likely seek an increase of about 5 percent in its next fiscal year.

In a Friday interview, Randall said her group still had heard no response from the mayor’s office. A spokesman for Bloomberg did not return phone calls.

While Randall acknowledged that lifting the budget from $3 million to $4 million was a sizable jump, she emphasized this would be the first increase in the FCBID’s existence.

“Thirty-three percent seems horrendous, but it’s not if you amortize it out over eight years,” she said. “Up until three years ago, when Giuliani stopped giving out increases at all as a matter of policy, many BIDs every single year got an increase. Our board was conservative and didn’t want to handle it this way. So eight years later, it’s sort of a horrendous amount, but you have to view it from the point of view that the services have increased.

“We would not anticipate having an increase at this level ever again,” she added.

The BID last sought an increase of $750,000 in 1999. That hike was turned down by the Giuliani administration.