The Taliban has ruled out any talks as long as foreign troops remain in Afghanistan.
Karzai said on Sunday that the condition was "unacceptable".
Zabiullah Mujahid, another Taliban spokesman, confirmed the group's position, saying Karzai's statement is not new.
"He has been saying this for the past seven years. But no brave fighter will accept this and we will not respect any law or constitution made by infidels," he said.
"The Islamic Emirate of Afghanistan will continue its jihad until foreign forces are out of Afghanistan and Afghanistan is independent."
Analysts say Karzai's safe-passage offer is not so much in the expectation that Omar would take up the offer, but to emphasise his message to other Taliban.
Karzai also hopes to win a presidential election next year and wants to be seen by a war-weary electorate as making every effort to bring peace, analysts say.
At least 70,000 foreign troops, around half of them American, are struggling against the Taliban, whose influence and attacks are spreading in the south, east and west.
| Three bomb attacks killed several people on Monday in southern Afghanistan [AFP]
Barack Obama, the US president-elect, has suggested that he is open to holding talks with more moderate Taliban leaders to explore whether the Iraq strategy would work in Afghanistan.
A tentative first step towards talks was taken in September when a group of pro-government Afghan officials and former Taliban officials met in Saudi Arabia for discussions on how to end the conflict.
But the Taliban derided those talks and repeated their demand that foreign troops leave Afghanistan.
However, Afghan government officials have said they expected another round of talks to be held.
On the ground, there has been no let-up in violence. A roadside bomb aimed at Afghan soldiers in Panjwayi, a district in the southern province of Kandahar, killed four civilians, while a suicide bomb attack in the same region killed three other people, an official said.
The attack on the Afghan army patrol lightly damaged their vehicle, and instead hit a nearby group of civilians, Zalmai Ayubi, the Kandahar governor's spokesman, said.
Four civilians were killed and eight others were wounded in the explosion, Ayubi said. He accused the Taliban of planting the bomb.
In the second attack in Kandahar, two police officers and a civilian died when a suicide bomber blew himself up at the entrance of a government office in the district of Dand, Ayubi said.
Three other police were wounded when officers tried to stop the bomber from entering the offices of the district chief, he said.
The Kandahar governor's office told Al Jazeera that the attacker had disguised himself in a police uniform and attempted to enter the district chief's office.
He was shot by police but was still able to detonate his explosives.
The previous day, a suicide attacker killed two Afghan civilians and wounded two German soldiers serving with Nato in the northern province of Baghlan.
Two US soldiers were injured on the same day in a bomb attack on the outskirts of the western city of Herat, the US military said.