(CNN) -- Attempting to advance his nation's peace progress with insurgents, Afghan President Hamid Karzai said unofficial talks with the Taliban have been taking place, and hopes the formation of a peace council will further those efforts.
"We have been talking to the Taliban as countryman to countryman, talk in that manner," Karzai told CNN's "Larry King Live" in an interview aired Monday night. "Not as a regular official contact with the Taliban with a fixed address, but rather unofficial personal contacts have been going on for quite some time."
"Afghanistan is once again the home for all Afghans. And the Taliban as Afghans are welcome," said the president, speaking from Kabul.
Karzai also spoke on the High Peace Council, an initiative headed by former Afghan President Buhanuddin Rabbani and tasked with boosting negotiations with Taliban insurgents.
"The Taliban, those of whom who are Afghans and the sons of Afghan soil, who have been driven to violence by various factors beyond their control and beyond ours caused by circumstances in Afghanistan, we want them to come back to their country," Karzai said.
"They are like kids who have run away ... from the family. The family should try to bring them back and give them better discipline and incorporate them back into their family and the society. President Rabbani assuming chairmanship today of the peace council is exactly in that spirit."
However, the Afghan government will work against groups like al Qaeda, Karzai said. "Those who are a part of al Qaeda and the other terrorist networks who are ideologically against us or who are working against Afghanistan knowingly and out of the purpose of hatred and enmity -- those of course we have to work against."
Karzai's remarks about the unofficial contacts with the Taliban came when the president was asked about a Washington Post report that secret high-level talks between the government and the Taliban were underway.
"Now that the peace council has come into existence, these talks will go on, and will go on officially and more rigorously, I hope," Karzai said. "But no official contacts with a known entity that reports to a body of Taliban and that comes back and reports to us regularly. That hasn't happened yet and we hope we can begin that as soon as possible."
The Afghan president denied a report that he has been diagnosed as manic-depressive in a book by veteran Washington journalist Bob Woodward. In his book "Obama's Wars," Woodward cited U.S. intelligence reports. "He's on his meds; he's off his meds," Woodward quoted U.S. Ambassador Karl Eikenberry as saying about Karzai.
"The only medication that I have taken is an antibiotic called Augmentin," when suffering from a cold two years ago, Karzai told King. He added that from time to time, he also takes vitamin C, multivitamins and Tylenol, "when I have a headache or when I'm tired."
He denied being manic-depressive, calling the story "rather funny."
Asked about the planned drawdown of U.S. troops in Afghanistan next summer, and relations with President Barack Obama, Karzai said, "Relations with President Obama are very good" and the two are in regular contact and had a video conference a few days ago.
"The relation with the U.S. government is generally good," he said. "There is a strategic relationship between us, partnerships towards an objective -- that's security for us and security for the United States and the rest of the world."
"On the staying power of the United States in Afghanistan, the Afghan people have been abandoned before when we fought the Soviets," he said. "When we defeated communism and the Soviets, the international community supported us, but then after their defeat we were abandoned and forgotten immediately, including by the United States."
He said the fear the same thing could happen lingers among the Afghans, and he has not been able to reassure them.
"I hope the United States of America and our other allies will help us through good means so we can reassure the Afghan people that this partnership is staying and that Afghanistan will emerge out of this current transition into a better country, a better economy and a more stronger, effective state," Karzai said.