Safar al-Hawali said he was still negotiating by phone on Thursday evening with Salih al-Awfi, believed to be al-Qaida's leader in the kingdom, to persuade him to give up.
"I am now negotiating with al-Awfi. He may surrender before midnight," al-Hawali said. He said he had asked authorities to extend the deadline but Crown Prince Abd Allah had refused.
The amnesty aimed to end al Qaida-linked attacks in the world's biggest oil exporter. It came after security forces killed Abd al-Aziz al-Muqrin, al Qaida's leader in Saudi Arabia, and three others after they executed US hostage Paul Johnson.
Al-Awfi is believed to have taken over leadership of al-Qaida in Saudi Arabia after al-Muqrin's death. The Interior Ministry said this week it had detained Awfi's wife and three children.
Prince Abd Allah had warned dissidents loyal to Saudi-born Usama bin Ladin's network to take advantage of the amnesty or face a renewed crackdown when it expired.
"I am now negotiating with al-Awfi. He may surrender before midnight"
"The Interior Ministry wishes to draw attention that the deadline of the (amnesty) call made to those who had strayed off the path of Islam expires on Thursday evening," an Interior Ministry statement said.
Only four are confirmed to have surrendered since the amnesty was declared by de facto ruler Crown Prince Abd Allah.
Interior Minister Prince Nayif bin Abd al-Aziz had said he expected large numbers to give themselves up. Al-Qaida in Saudi Arabia had said in Internet statements the initiative would fail.
Al-Harbi surrendered in Iran
Al-Qaida supporters have waged a 14-month campaign of human bombings in Saudi Arabia against foreigners, state institutions and the oil industry. Some 90 policemen and civilians, many of them foreigners, have been killed.
Two have surrendered in Saudi Arabia, one in Syria, and a fourth, Khalid al-Harbi, in Iran. Al-Harbi appeared with bin Ladin in a videotape praising al-Qaida's September 11 attacks.
Uthman al-Amri, who is on Saudi Arabia's list of 26 most wanted dissidents, gave himself up at al-Hawali's Jidda home on 28 June.
Al-Hawali said a fifth who surrendered at a Saudi embassy in an unspecified Arab country had arrived in the kingdom on Thursday.
Officials said the state would drop its claims against those who surrendered but that families of their victims could still press for punishment.