Shaukat Aziz, Pakistan's prime minister, is in Kabul for the meeting, taking Musharraf's place.
In his opening address to the council, Karzai appealed for a spirit of partnership between Afghanistan and Pakistan to deal with the Taliban and al-Qaeda.
"I am confident, I believe... if both Afghanistan and Pakistan put their hands together, we will eliminate in one day oppression against both nations," Karzai said.
"If the problem is from the Afghanistan side, we should seek ways to solve it. If the problem is in Pakistan, we should find solutions for it"
Hamid Karzai, president of Afghanistan
"If the problem is from the Afghanistan side, we should seek ways to solve it. If the problem is in Pakistan, we should find solutions for it."
The three-day jirga was agreed by Musharraf and Karzai in Washington last year to bring leaders together to seek a strategy against al-Qaeda and Taliban forces.
Dan Nolan, Al Jazeera's correspondent in Kabul, said Musharraf's no-show had been badly received by some jirga delegates.
"On the record, jirga delegates are saying [Musharraf's absence] will not affect the jirga in any way, but off the record some have indicated that they feel betrayed by his decision not to come and they see the sending of the Pakistani prime minister instead as a token gesture," he said.
"Some believe Shaukat Aziz is not exactly up to speed with the issues along the tribal areas, which is what this jirga is all about."
The council meeting has already been boycotted by some Pakistani tribal groups.
Afghan officials have accused Pakistan of harbouring Taliban and al-Qaeda fighters in order to keep its neighbour weak and reinforce its regional power.
Pakistan rejects the accusation and says it has arrested several al-Qaeda leaders.
Islamabad says it is fighting the Taliban in tribal areas along the disputed Afghan border.
About 175 Pakistani officials, politicians and tribal elders are to attend the jirga, in a large marquee in the Afghan capital.
A similar number of Afghanistan representatives will attend the council. A similar gathering will be held in Pakistan, but no date has yet been set.
|Karzai [left] and Musharraf agreed to the |
meeting last year in Washington [EPA]
Analysts and diplomats have warned against high expectations from the jirga, calling it a first step towards a unified approach on dealing with Taliban fighters and their al-Qaeda allies which threaten both countries.
A jirga is a traditional meeting among Pashtun tribes that live on both sides of the international border.
About 2,500 police are guarding the council meeting and Nato troops are on standby.
Security for the meeting will be tight for fear of attacks by the Taliban, who have renewed efforts to destabilise Afghanistan's government in the last year.
Taliban fighters are holding 21 South Koreans and a German hostage and have already killed three of their captives.