"I request the Taliban to lay down their arms and the government will solve their problem. They have lost commanders ... who were captured. It is time for them to stop fighting.
"If you refuse to surrender, the operation will take place and we will clear the area of the Taliban."
Al Jazeera's Zeina Khodr, reporting from Kabul, also quoted Omar as confirming that the Taliban's "shadow" governors of Kunduz and Baghlan had been captured in Pakistan.
The men were captured in Quetta and "the governor is predicting victory", she said.
Amid the talk of political reconciliation, Mullah Abdul Salam Zaeef, a former Taliban ambassador to Pakistan, has said that the Kabul government must remove "obstacles" if it wants to succeed in resolving the conflict through peaceful means.
"If [Hamid] Karzai [Afghan president] really wants to talk to the Taliban, he has to move the obstacles in the way," he said in an interview to Al Jazeera.
Zaeef said the question of "blacklist, wanted list and also the reward list" had to be addressed and that the UN had to recognise the Taliban.
The Taliban recently called Afghan overtures for talks "futile" and "farcical", although it says it is open to dialogue to achieve its goal of an Islamic state.
The developments come as a joint 1500-strong force of Afghan, US and Nato battles the Taliban in the Afghan city of Marjah in Helmand province.
The Taliban is said to be still putting up resistance.
Drug dealers' den
US officials said Marjah, which has been in control of the Taliban for years and is a den for drug dealers, has been secured and that a new administration would be installed in weeks.
But Al Jazeera's James Bays in Helmand said the "low military progress and the fact that they still have to clear a lot of area of mines" would make it hard to install a government.
Nato forces say the offensive, in which 15 Afghan civilians have died, is aimed at re-establishing Afghan government control so security and civil services such as police stations, schools and clinics can be set up.
Officials have reported the deaths of only two international forces troops during the operation so far, with one American and one Briton killed on Saturday.