U.S. envoy, Afghan president meet for 2nd day to discuss peace January 22, 2012 -- Updated 0754 GMT (1554 HKT) Marc Grossman, U.S. special envoy for Afghanistan and Pakistan, is in Kabul to talk with Afghan president Hamid Karzai.. Marc Grossman meets the Afghan President Hamid Karzai for a second day Karzai: The government and its peace council are making an effort to attain peace Secret talks between the United States and the Taliban have taken place since 2010 Kabul, Afghanistan (CNN) -- Afghan President Hamid Karzai meets a top U.S. envoy for a second day Sunday to discuss ways to end bloodshed and achieve a peaceful resolution to Afghanistan's conflict. Marc Grossman, the U.S. special envoy to Afghanistan and Pakistan, also met with Karzai on Saturday. During the meeting, the president made clear that Afghans should be in the driver's seat in finding a solution, saying the government and its peace council are making every effort to bring an end to the bloodshed. "The Afghan nation is the owner of the peace process and any peace talks," Karzai said. No other country or organization has the right to deprive the Afghan nation to this right. Afghanistan is not a place for foreigners to do their political experiments or a laboratory that every few years they test a new political system. Karzai recently met with the party of warlord Gulbuddin Hekmatyar, head of the militant Hizb-i-Islami group. "It was a positive meeting and happened in a good atmosphere," said a senior Afghan official with direct knowledge of the talks. The official, who did not want to be identified because the talks were confidential, said Hizb-i-Islami supports the process of negotiating with the armed opposition and more talks are planned. The meeting with Hekmatyar served as a signal from Karzai to the United States that peace talks encompass other radical groups besides the Taliban. Hizb-i-Islami has attacked U.S. forces, and Hekmatyar is on America's most-wanted list of terrorists. Karzai's spokesman Aimal Faizi declined to give details of the talks with Grossman. Secret talks between the United States and the militant Taliban began in November 2010, sources said. Grossman's visit comes days after Pakistan's government, embroiled in a squabble between civilian and military leaders, declined a visit from Grossman, saying it would fuel anti-American sentiments. CNN's Nick Paton Walsh and Elise Labott and journalist Nasir Habib contributed to this report.