The influential Sunni Arab religious group in Iraq said that before talks could begin, a calendar for the withdrawal of foreign forces must be established, according to a statement released after Friday's meeting.
Another condition for the Sunni group was to "consider resistance as a legitimate right and terrorism, in all its forms, as an inacceptable crime".
Iraqi fighters are often close to Sunni groups opposed to the US presence in Iraq, though some Muslim fighters such as al-Qaida front man Abu Musab al-Zarqawi have also called for an all-out war against Shias.
The committee wants to "rebuild the Iraqi army by getting rid of undesirable elements", and sought "the dissolution of armed militias that preach political sectarianism", a reference to Shia groups such as the Badr Organisation or Mahdi Army.
Other demands centred on the situation of Iraqis held by US-led forces, and independent commissions to probe crimes by members of Iraq's security forces.
Moussa met the committee directors at the Um al-Qura mosque in western Baghdad after the Friday prayer.
Speaking after a visit to the premises of the AMS and a meeting with its secretary-general, Harith al-Dhari, and a number of religious and tribal leaders, Moussa said: "The conditions set for the success of the proposed reconciliation conference in Iraq constitute proposals that can be negotiated."
Moussa (L) met Prime Minister
al-Jaafari and other top officials
Aljazeera quoted Moussa as saying he could feel a positive response for the proposed conference. "There were no conditions set for the proposed conference by any party," he said.
Meanwhile, Iraqi officials have issued a caution response to the league's offer of a national reconciliation conference for the country.
Aljazeera reports that Prime Minister Ibrahim al-Jaafari said on Thursday after meeting Moussa that he saw no fundamental problem with such a meeting, but ruled out participation by "terrorists" or former senior members of the disbanded Baath Party of former president Saddam Hussein.
Moussa is due to travel to Iraqi Kurdistan to meet its president, Massoud Barzani, in the next several hours.