A spokesman would not comment on Monday on the US-backed Council members' refusal to come to the pan-Arab organisation's headquarters in Cairo for talks with Mussa.
The slight may have come as a result of the Arab League’s reluctance to recognise the interim government officially, as well as its decision to keep Arab troops out of the US-led occupation.
"Mr Mussa has repeatedly said that the Arab League is open to all Iraqi political forces, including members of the Iraqi Governing Council," League spokesman Hisham Yussef told reporters on Monday, but avoided questions about the snub.
"We must begin by talking about the key issues of interest to the Iraqi people such as an end to the occupation, legislative elections, the drafting of a constitution and reconstruction," Yussef said.
On Thursday council member Mowaffak al-Rubaiei told Agence France Presse that each member of the US-appointed 25-strong transitional authority had received an invitation to meet Mussa in Cairo.
"We will not go except as an official delegation"
Mowaffak al-Rubaiei, Governing Council member
"The league has addressed invitations to each of us to meet Secretary General Amr Mussa, but we will not go except as an official delegation of the transitional Governing Council representing Iraq," al-Rubaiei told Agence France Presse.
Arab foreign ministers who met at League headquarters in Cairo on August 5 to discuss the post-war situation in Iraq avoided an official recognition of the Council and turned down US requests to send Arab troops to Iraq.
Following a meeting with his Saudi and Syrian counterparts on August 11, Egyptian Foreign Minister Ahmed Maher said Arab states could not give the Council their unqualified support because it was not a "legal authority."
The UN Security Council Thursday adopted a resolution that welcomed the establishment of the Governing Council but stopped short of formally endorsing the body, as initially sought by the United States.