NEW YORK — A 750-foot glass-and-steel office tower — with better fireproofing and wider stairs for quick evacuation — will be built on the site of one of the smaller buildings to collapse at the World Trade Center complex.

The plans, unveiled Wednesday, represent the first major rebuilding project at the World Trade Center to be announced.

The 52-story building at 7 World Trade Center — across the street from the main trade center site — will be sleeker and five stories taller than its predecessor, which collapsed in a raging fire several hours after the twin 110-story towers were destroyed in the Sept. 11 attack.

“The fact that this building is going up now and going up here, right on the site of the old No. 7, says that we will not be intimidated by the terrorists,” Mayor Michael Bloomberg said.

Architects are still laboring to create designs for the larger trade center site. Although those plans will not be made final until next year, developer Larry Silverstein and his architect, David Childs of Skidmore Owings ‘ Merrill, said their design for 7 World Trade would serve as a model.

The main site is owned by the Port Authority of New York and New Jersey; Silverstein is the leaseholder.

The new building, scheduled to open in late 2005, has been designed with stairs 20 percent wider than required by the city code, sturdier fireproofing than required, and an internal antenna system for improved communication by firefighters and police. Rescuers have complained of radio trouble on Sept. 11.

The first 10 stories will be occupied by a Con Edison power company substation; other tenants have not been determined. The original 7 World Trade Center housed a Con Ed substation, the mayor’s Office of Emergency Management and other government and financial offices. It had been evacuated when it fell, and no one died there.

Silverstein said that $800 million in insurance proceeds will cover most of the new building.