Emaar Properties said the 512m (1,680ft) Burj Dubai is now taller than Taiwan's 508m (1,667ft) Taipei 101.
It is thought Burj Dubai will eventually be 693m (2,275ft) tall.
Height records are contentious, with dispute over what defines a "building" and what is being measured - height to the top floor or the tower's antenna.
When finished the building is expected to meet the Council on Tall Buildings and Urban Habitat's four criteria - the height of the structural top, highest occupied floor, the roof's top, and the spire's highest point - to become the world's tallest structure.
"Burj Dubai has now reached 141 storeys, more storeys than any other building in the world," the company said in a statement.
There is speculation that, spire included, the final height could be more than 800m, but Emaar is keeping structural details secret.
'Symbol of Dubai'
When finished, the skyscraper will have more than 160 floors, 56 elevators, apartments, shops, swimming pools, spas, corporate suites, Italian fashion designer Giorgio Armani's first hotel, and an observation platform on the 124th floor.
"It's a fact of life that, at some point, someone else will build a taller building"
To qualify as a building, a structure has to have floors and walls all the way to its roof.
The tower is also expected to break the record for highest man-made structure, currently held by the wire-assisted KVLY-TV mast in North Dakota, US, which is 628m (2,072ft) tall.
"It's a symbol of Dubai as a city of the world," Greg Sang, the project director for Emaar Properties, was quoted as saying by the Associated Press.
Chairman Mohammed Ali Alabbar said Dubai has "resisted the usual and has inspired to build a global icon," according to AP.
"It's a human achievement without equal."
Building began on the structure on 21 September 2004, and is expected to be completed in 2008.
The spire of the building is expected to be able to be seen from 100km (60 miles) away.
"It's a fact of life that, at some point, someone else will build a taller building," Mr Sang said.
"There's a lot of talk of other tall buildings, but five years into Burj Dubai's construction, no one's started building them yet."
Previous skyscraper record-holders include New York's Empire State Building at 381m (1,250 ft); Shanghai's Jin Mao Building at 421m (1,381 ft); Chicago's Sears Tower at 442m (1,451 ft) and Malaysia's Petronas Towers at 452m (1,483 ft).
The CN Tower, in Toronto, Canada, is the world's tallest freestanding structure, at 553m (1,815.3 ft).
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