Once the excavations are completed, Israel plans to build a pedestrian bridge to the complex to replace a ramp damaged in a snowstorm and an earthquake in 2004.
Jews revere the compound, overlooking Judaism's Western Wall, as Temple Mount, where two destroyed biblical temples are believed to have once stood.
'All possible speed'
The official said: "The government approved continuation of construction at the approach to the Mughrabi Gate [leading into the complex] within the proposed framework, at all possible speed."
Your Views "The daily teachings of suffering and hatred must be replaced with tolerance and co-existence" Docdeb, NY, USSend us your viewsThree ministers voted against pursuing the work, he said.
"The daily teachings of suffering and hatred must be replaced with tolerance and co-existence"
Docdeb, NY, USSend us your views
On Friday, some 200 Israeli police wielding batons clashed with protesters who threw stones at them at the plaza outside al-Aqsa, in a confrontation in which 17 Palestinians and 15 police officers were injured.
During that protest, police also evacuated Jewish worshippers from the Western Wall site.
Before the cabinet vote, Ehud Olmert, Israel's prime minister, said in broadcast remarks that the ramp was a dangerous structure that needed renovating.
He said: "There is no religious issue here" and accused "Arab extremists" of inciting violence.
In East Jerusalem, Israeli police confronted protesters for a third straight day and arrested five, said Micky Rosenfeld, a spokesman for the national police.
Arab condemnation
The Arab League condemned the dig at a meeting in Cairo on Saturday and demanded Western nations force Israel "to stop this aggression immediately".
The Jerusalem compound has frequently been a flashpoint for Israeli-Palestinian violence.
A Palestinian uprising erupted in 2000 following protests at the complex after Ariel Sharon, then a candidate for the prime minister's post, visited the site as head of Israel's opposition party.
Israel captured East Jerusalem in a 1967 war and annexed it in a step not internationally recognised.
Palestinians want the eastern part of the city as the capital of a future state.