Mansour Dadullah was appointed as the new field commander by the Taliban after Mullah Dadullah was killed by the coalition forces.
"Sheikh Osama prefers not to be seen or meet anyone because if he makes himself available to the media maybe he will be facing danger.
"His presence is an honour to all of us, we don't want to lose him. I have also asked him not to meet anyone and remain in hiding and continue to give his instructions to the commanders so that al-Qaeda would remain alive and continue its activities all over the world."
Meanwhile, the Taliban said it had beheaded an Afghan doctor and warned of more bloodshed after the government failed to hand over the body of Mullah Dadullah.
The Taliban had earlier threatened to execute the doctor and three male nurses, who were captured in late March, if the corpse of Dadullah was not handed over by Tuesday morning.
Shohabudin Atal, the Taliban spokesman, said: "We had told the government to hand over the body of Dadullah. Since they didn't hand us the body, we beheaded one of the doctors named Abdul Khalil."
There was no independent confirmation of the Taliban claim.
After Mullah Dadullah's body was shown to the media, he was buried at a secret location in the southern province of Kandahar.