Deiss and Ambassador Ge'rard Araud of France, which holds the rotating Council presidency during May, met on Wednesday and discussed the situations in Syria, Libya, Sudan, Somalia, Cote d'Ivoire and the Democratic Republic of the Congo (DRC), among others.
The two officials exchanged views on global governance, Security Council reform and the thematic debates convened during the 192-member Assembly's current session, and they also discussed the Council's visit to Africa later this month.
Meanwhile, Deiss told an open briefing on the United Nations Counter-Terrorism Implementation Task Force (CTITF) on Thursday that Member States need to make "substantive progress" to finalize a comprehensive convention against terrorism.
He noted that the UN global counter-terrorism strategy, adopted by consensus by Assembly members in 2006, represents "the first document in which the entire membership expressed a clear position on the strategic approach to counter-terrorism."
Deiss said the key challenge now is to ensure the effective implementation of that strategy, and he said the CTITF should be integral to those efforts.