Saudi Arabia's amnesty for Islamic militants to turn themselves in expired at midnight (2100GMT) on Thursday.
Oufi is suspected of being involved in clashes with police on Wednesday
Only a few have surrendered, but a mediator said he was still negotiating with some militants - including the alleged local al-Qaeda leader.
Mediator Sheikh Safar al-Hawali said earlier there was optimism that Saleh Mohammed al-Oufi would give himself up.
King Fahd declared the amnesty in June, but officials have vowed to strike "with full might" when it runs out.
Fayez al-Khushman was the fourth to give himself up, on Thursday evening in the city of Taef.
Mr Oufi is thought to have taken over the leadership of al-Qaeda in Saudi Arabia a month ago after his predecessor, Abdulaziz al-Muqrin, was killed by police.
He is suspected of being involved in clashes with police in the capital Riyadh on Wednesday which led to the arrest of his wife and three children.
The other two suspects negotiating their surrender - who feature on a list of the 26 most wanted militants - prefer to remain anonymous, Mr Hawali said.
'Public relations exercise'
The BBC's Middle East analyst says that the amnesty failed to draw the kind of response the Saudi authorities had hoped for.
They had always realised the most hard-line figures within what they regard as the local wing of al-Qaeda were unlikely to heed it. And indeed in their statements on the internet, radical leaders poured scorn on the idea of surrendering to a government they habitually describe as "apostate".
But officials had hoped that younger - less ideologically hardened - militants might be more open to calls coming not just from the government, but from religious leaders and in some cases family members.
The amnesty was always something of a public relations gesture, our Middle East analyst says. It enabled the country's ruling princes to claim they were ready to be magnanimous to those who gave up violence, while warning they would act with a new severity against those who refused.
The wave of attacks by Saudi militants over the last year has killed about 90 people, many of them foreigners. The militants' aim is to drive foreigners from the kingdom and topple the ruling House of Saud.