The statement from Arabtec came a day after reports - that it said were incorrect - alleging that Aabar, owned by the Government of Abu Dhabi, had taken a controlling 53 per cent holding.
The Abu Dhabi investment company declined to comment.
In a statement posted on the Dubai Financial Market yesterday, Arabtec said the sovereign wealth fund held a combined 20.76 per cent through four investment vehicles.
Arabtec shares leapt 4.6 per cent to Dh2.91 each following the announcement, having fallen 5.7 per cent the previous day.
On Sunday, Khadem Al Qubaisi, the chairman of both Arabtec and Aabar, was quoted in the newspaper Alrroya as saying that Aabar had taken a 53 per cent stake.
But the Arabtec statement distanced the company from that. "The newspaper article posted in Alrroya Aleqtissadiya 'Aabar acquires 53 per cent of Arabtec' on 12/05/2012 includes incorrect information," Arabtec said.
"Aabar's companies investments in Arabtec Holding through its investments funds totals is 20.76 per cent, according to the share register settlement 10/05/2012," it added.
Aabar representatives declined repeated requests for comment to explain the discrepancy between the two statements. Mr Al Qubaisi was appointed the chairman of Arabtec last Wednesday. Farah Al Obaidi, an Arabtec spokeswoman, declined to comment on the contrasting totals.
Arabtec's shares have soared by as much as 128.3 per cent this year as reports of an accumulation of shares by a big investor - now known to be Aabar - became an open secret on trading-room floors. The shares are up 92.1 per cent so far this year, following a recent sell-off.
Even including those declines, Arabtec's share price rise has accounted for about half of the gains on the Dubai Financial Market (DFM) General Index so far this year.
Later in the day, Aabar funds were disclosed by the DFM to have taken a total 20.93 per cent stake in Arabtec, after two Aabar-linked vehicles disclosed a 10.43 per cent stake.
The newest shareholdings are split between two companies, Aabar Energy and Aabar Petroleum Investments PJSC.
Arabtec and Aabar sought a tie-up in 2010, in a Dh6.4 billion (US$1.74bn) deal which would have resulted in Aabar taking a 70 per cent stake in the construction company.
However, the companies walked away from the deal within a few months of its announcement, declining to give an explanation.
At the time, the companies said they would seek a "strategic partnership in Abu Dhabi" instead.
This month, Arabtec was announced as one of the three companies forming a consortium that is the preferred bidder for the construction of a new terminal at Abu Dhabi International Airport.