In response to the charges, Moustafa told the courtroom in central Cairo: "It did not happen and I have presented all the evidence that I am not guilty."
"It did not happen," said Sukkari. "By Almighty God my blood is innocent of her."
The two defendants appeared in metal cages in the courtroom.
The Egyptian judiciary is trying the case because Egyptian law does not allow the extradition of Egyptian citizens to face trial in other countries.
Al Jazeera's Amr El-Kahky, reporting from outside the courtroom, said that there is intense interest in this case.
"Many Egyptians are very curious to see what the verdict for this case will be, considering Moustafa's well-known ties to the higher echelons of the Egyptian political establishment," he said.
"Moustafa is well connected to Gamal Mubarak, the president's son, so there is obviously interest regarding the independence of the judiciary in this case."
The indictment says Sukkari killed Tamim after tricking her into opening the door of her Dubai apartment by posing as a representative of the building owners.
"He then attacked her with the knife ... cutting her main arteries and her trachea," it said.
"This was on the instigation of the second defendant [Moustafa] in return for obtaining from him the sum of $2 million for committing this crime."
Egyptian media reports have said that Sukkari worked as a security officer at the Four Seasons Hotel in the Red Sea resort of Sharm el-Sheikh, which the Talaat Moustafa Group built.
The indictment said Moustafa "took part through incitement, agreement and assistance with the first defendant [Sukkari] in killing the victim in revenge".
"He provided him with special information and amounts of money necessary to plan and carry out the crime," it said.
The evidence includes tape recordings of telephone calls between Moustafa and Sukkari, security video footage from the Dubai apartment and DNA from the bloodied clothes that Sukkari allegedly left close to the scene of the crime.
Moustafa, who was born in 1959, has given up the chairmanship of the Talaat Moustafa Group to Tarek, his brother, and has been stripped of the legal immunity he enjoyed as a member of the upper house of parliament.
Tamim, who was 30, rose to fame after winning the top prize in a television show in 1996.