The statement, carried by the official Saudi Press Agency, said preparations by the suspects had "reached an advanced stage".
They included attempts to find hideouts for their cells, forging travel documents and launching an internet campaign to spread their "deviant ideology".
Some in the group collected money to finance their activities under the guise of charity, according to the statement.
State television also aired part of the audio recording, which SPA said was brought into the kingdom on the mobile telephone of a "person who had visited Mecca".
Security forces have now rounded up a total of 56 members of the group who are of "various nationalities," including their leader, the Saudi ministry added, without naming its chief.
Samir Al-Saadi, a security correspondent for Arab News, told Al Jazeera that there is an ongoing investigation into the suspects.
"One of them was a foreigner arrested outside the kingdom, he had an SMS message from Ayman Zawhri to get funds.
"The interior ministry is worried that al-Qaeda is trying to reorganise itself in Saudi Arabia," he said.
Police interrogated the first 28 suspects in December after an alleged plot to carry out a "terrorist" attack during Hajj, the annual Muslim pilgrimage to Mecca.
Arrests were made in the provinces of Mecca, Medina, Riyadh and the area around the kingdom's northern borders, police said.
In November, Riyadh said it had arrested 208 suspected al-Qaeda fighters who were plotting assassinations and an attack on a logistical oil facility.
Saudi Arabia has been battling suspected al-Qaeda fighters since several shooting and bombings took place in May 2003.