Ali Yunesi, speaking to reporters in the capital, Tehran, on Saturday, did not specify when the 3000 members of the group were dealt with by Iran.
But the number is the largest Iran has provided of members of Osama bin Laden's network being in the country.
Iranian officials normally are tightlipped on security affairs, and Yunesi's comments follow claims by US and foreign intelligence agencies that mounting evidence gathered over several years has them increasingly convinced that leading "terror suspects" have been living in Iran.
State-run Iranian TV showed Yunesi's picture as an announcer quoted the minister announcing that Iranian courts had tried al-Qaida members and jailed and deported some. Others were apparently still in detention pending further legal action.
None of the al-Qaida members was identified and no further details were provided by the television station.
Iranian officials were not immediately available for comment.
On 6 June, another senior Iranian official revealed that 500 al-Qaida operatives had been arrested during the past three years and had been handed over to their home countries.
Hasan Rowhani, head of the Supreme National Security Council, said the suspects had been hiding out in Iran, which had given the names of the detainees to the United Nations.
Iran has denied reports that Abu
Musab al-Zarqawi was in Iran
Iran denies US claims that it has been harbouring "terrorists", saying it has been cooperating in combatting terrorism and received praise from international bodies. Iran first said in mid-2003 that it had detained and deported hundreds of al-Qaida suspects and kept some in custody.
US officials have said Iran refuses to identify the al-Qaida operatives that are still in its custody.
In June, Iran denied reports that Abu Musab al-Zarqawi, al-Qaida's leader of the Iraqi resistance, was in Iran after being wounded.
Iran has been under increasing pressure to curb its nuclear program, which the United States claims is aimed at building atomic bombs. Tehran denies such claims, stressing that its nuclear activities have peaceful purposes, including generating electricity.
Yunesi, in separate comments to the state-run Islamic Republic News Agency, claimed that several Iranian nuclear experts had been "trapped" during visits abroad and that the United States and Israel were trying to recruit their scientists.
"Both the US and Israel tries to recruit Iranian nuclear experts," Yunesi was quoted as saying.
"They (the scientists) have to be aware and not to be trapped during their visits abroad. Unfortunately a number of scientists were trapped by foreign intelligence services and we are trying to save them," he added.
Yunesi did not identify the experts or say when or where they were "trapped." His claims mark the first time Iranian officials were unaware of the whereabouts of their scientists in other countries.