Karzai made his offer on Saturday, hours after one of the worst attacks in the Taliban's near six-year armed campaign killed 30 people in Kabul, the capital.
 
Meeting proposed
 
Back from a trip to the US, Karzai said he was ready to meet Mullah Mohammad Omar, the Taliban's fugitive leader, and Gulbuddin Hekmatyar, the chief of another anti-government group, for peace talks.
 
In video

Al Jazeera's Alan Fisher reports on the daily perils faced by US forces in Afghanistan

But he excluded any pre-conditions such as the withdrawal of nearly 50,000 troops under the command of Nato and the US military, as demanded by fighters.
 
Karzai said George Bush, the US president, and Ban Ki-moon, the UN secretary-general, had both supported the idea of peace talks when he met them in the US this month.
 
But Yousuf said: "On the one hand, America has put our leader's name on a wanted persons list and is calling us terrorists; and on the other hand, Karzai is talking about peace talks. It's a joke."
 
Both Mullah Omar and Hekmatyar are wanted by the US.
 
Cabinet posts
 
Karzai had said he would allocate some government posts to the Taliban and that both Hekmatyar and Omar could stand in the elections, due to be held in 2009, if they wanted power.
 
He is eager to end the violence, which has claimed around 5,000 lives so far this year, most of them of Taliban members, compared with about 4,000 last year.
 
People gather at the blast site
as a clear up operation starts [Reuters]
Despite the Taliban's rejection, Homayun Hamidzada, Karzai's spokesman, said on Sunday that the government "knew" there was debate developing among  some factions in the Taliban - although not those linked to al-Qaeda - about talks.
 
"Not all of them, not al-Qaeda, but there's serious debate among some Taliban groups," he said.
 
"We don't expect something to happen  now. This is a process which will take time."
 
Meanwhile, violence continues unabated in the country.
 
Two police officers were killed on Sunday trying to defuse a bomb outside the troubled southern city of Kandahar, police said.
 
Two more security officers were wounded, Abdul Hakim Angar, the deputy police chief, said at the site of the blast.
 
An Afghan television journalist filming there was badly hurt.
 
Patrol attacked
 
On Saturday, two Afghan women and a child were killed when the Taliban attacked an Afghan army patrol in the country's east, Din Mohammad Darvish, a spokesman for Paktia province, told the AFP news agency.
 
International soldiers were called to repel the attack.
 
"Seven Taliban were killed in raids," Darvish said.
 
The Nato force in Kabul announced a foreign soldier was killed in the same area, but it would not confirm whether it was the same incident.
 
In other news, the Danish Army Central Command said on Sunday that two Danish soldiers killed earlier this week in Afghanistan may have been the victims of "friendly fire".
 
The soldiers were killed on Wednesday in Helmand province in southern Afghanistan when Taliban forces attacked Danish positions several times.
 
The Danish army said in a statement on its website: "There is a suspicion that the Danish unit during the fight with the Taliban was also under fire from another ISAF (International Security Assistance Force) unit."