Omar is believed to be in hiding in Pakistan but has not been seen in years.
Eid olive branch
In his own public statement on Sunday, Hamid Karzai Afghan, the Afghan president, called on the Taliban to end the conflict.
"On this auspicious day, once again I ask all those Afghan brothers who are unhappy or are in others' hands to stop fighting, destroying their own land and killing their own people," he said at the presidential palace in Kabul.
"They must come to their houses and live in peace in their own countryl".
Karzai said should he win another five years as president, he would launch peace talks with Taliban leaders, whose anti-government campaign has intensified in recent months to deadly effect.
His remarks came a day after the Danish military announced that one of its soldiers was killed after Taliban forces fired on troops on patrol in the southern province of Helmand.
Denmark has lost 25 soldiers in Afghanistan since it joined the US-led multinational force in 2002.
Separately, Hungarian officials said a suicide attacker drove a vehicle into a convoy in the northern city of Pul-e-Khumri. No soldiers were killed.
Extra US troops
Ambushes targeting international forces have become increasingly sophisticated and deadly in recent months.
Use of remote-controlled bombs has seen 2009 become the worst for foreign forces in the eight years of the war, with more than 350 deaths so far.
Barack Obama, the US president, has ordered 21,000 more troops to Afghanistan this year.
By the year's end, Washington will have a record 68,000 in the country.
The US and Nato commander in Afghanistan, General Stanley McChrystal, is expected to ask for thousands more troops in coming weeks, even though public support for the war is waning.