Speaking on Tuesday at a graduation ceremony, Nayef said the new suspects belonged to the same group of men involved in terrorist acts over the past two years.
His comments were reported by the official Saudi Press Agency on Wednesday.
"We cannot discount what these people can do. All our security forces are active and capable of getting to them. Any act they carry out will fail and we will determine who carries it out," he said.
The latest list included many young operatives who may have already fled abroad - possibly to Iraq - amid a fierce crackdown on al-Qaida's network in the kingdom.
Saudi authorities have been claiming success in their efforts to uproot insurgents who carried out a series of bloody attacks two years ago.
Security forces have killed or captured 23 out of 26 figures on the first wanted list put out in December 2003.
Nayef said the suspects on the list of 36 "participated in all the terror activities of the old list of 26... It is the same group and has the same instructions and they are totally connected to the old group but their execution may differ."
"We did not and have not said that terror acts are over"
Prince Nayef bin Abd al-Aziz, Saudi interior minister
One of the most significant figures on the new list was Muhsin al-Fadli, 24, a man Washington considers a leader in al-Qaida in the Arab Gulf region. It was the first word that al-Fadli, a Kuwaiti, was believed to have been in Saudi Arabia and involved in attacks there.
In February, the US Treasury moved to freeze al-Fadli's finances, accusing him of providing financial and material support to terrorist networks run by Jordanian-born Abu Musab al-Zarqawi, thought to be behind scores of attacks in Iraq.
Al-Fadli is one of 21 people on the list that the Interior Ministry said were believed to have fled the kingdom after participating in attacks.
Nayef warned that there could be even more dangerous individuals who have not been identified yet.
Prince Nayef (R): The suspects
participated in terrorist acts
"We did not and have not said that terror acts are over. Had they been over, we wouldn't have announced the new list. The possibility of more crimes still stands," he said.
Faris bin Hizam, an expert on Saudi "terrorist" groups, said it was likely that many of the 21 had slipped into Iraq to fight alongside fighters battling Iraqi and US forces, but Saudi officials said their whereabouts were unknown.
Saudis have made up a significant part of the non-Iraqi fighters in the Iraqi uprising, including some believed to have blown themselves up in attacks.
The ministry offered rewards of between 1 million riyals ($267,000) and 7 million riyals for information leading to the arrest of any of the suspects or foiling an attack.
The list includes 29 Saudis, three Chadian nationals, a Moroccan, a Kuwaiti, a Yemeni and a Mauritanian.
Saudi Arabia has suffered a series of attacks since May 2003 when bombers attacked three housing estates for foreigners in the capital Riyadh.
After the attacks, the kingdom issued its first list of 26 most wanted suspects in December 2003 and launched a wave of raids against militant groups.
Those remaining from the first list include Salih al-Aoofi, considered to be the top leader of al-Qaida's branch in Saudi Arabia, and Talib Saud Abd Allah al-Talib. Both men are Saudis.
Saudi Arabia is the birthplace of al-Qaida leader Osama bin Laden, and 16 of the 19 alleged hijackers involved in the 11 September 2001 attacks on the United States.