Sudan's government delegation was not immediately available for comment.
Last month a ceasefire agreement between the Jem and the Khartoum goverment was signed in Doha, but the Sudan Liberation Movement (SLM), another opposition Darfuri group, boycotted the signing ceremony.
Jem said forthcoming legislative and presidential elections in April should be postponed so the group and the millions suffering in Darfur from a seven-year conflict could participate.
"If the political will and decision is there we can reach an agreement as quickly as possible," al-Faki told the Reuters news agency on Tuesday.
Jem insisted it would not negotiate if there were parallel talks with other opposition groups - a reference to the SLM - unless they united under the Jem.
Al-Faki said direct talks with the Khartoum's delegation would flesh out the ceasefire declaration between the two sides.
"There are so many issues regarding the ceasefire which need to be discussed - numbers of troops, repositioning, redeployment," he said.
Al-Faki said Sudan's army, which on Monday declared it had taken control of the Jabel Marra region long controlled by the SLM, had already broken the ceasefire.
"The ceasefire agreement which we signed was in all of Darfur, not just in areas under the control of Jem," he said.
"We see this as an abrogration of the framework agreement."
The International Criminal Court (ICC) last year issued an arrest warrant against Omar Hassan al-Bashir, the Sudanese president, for war crimes in Darfur, where the UN estimates up to 300,000 have died in one of the world's worst humanitarian crises.|
Sudan disputes that figure and says only 10,000 have been killed.
Al-Bashir hopes a victory in April's presidential election will legitimise his government in defiance of the warrant.
However, al-Faki says elections cannot be free and fair with Darfur still under emergency law and al-Bashir in control of state finances and media.