Popular Congress number two Abdullah Hassan Ahmed told AFP he had met his counterpart from the ruling party, Ibrahim Ahmed Omar, on Wednesday and they had agreed to hold further talks.
The meeting marked a sharp change in policy towards the Islamists by the increasingly isolated military-backed government in Khartoum, which last year rounded up much of the Popular Congress leadership on charges of taking part in an alleged coup.
"Yes, I agree it could be a thaw," said Ahmed, who held a number of cabinet posts, including finance minister, before the split between Turabi and his one-time protege President Omar al-Beshir in 1999.
Ahmed told AFP the overture had come from the ruling party "apparently as part of a bid by the National Congress to consult political forces on current issues."
He said the talks had focused on implementation of a landmark peace agreement which the government signed with the rebel Sudan People's Liberation Movement in January, ending two decades of civil war with the mainly Christian or animist south.
He said he voiced "concern about the delay in implementing the agreement" which also provides for a new power-sharing government in Khartoum, involving not only the southern rebels but also other opposition groups.
"But we are now optimistic after the meeting with Omar and another meeting yesterday (Wednesday) with the visiting SPLM delegation, who said they were serious about implementation of the agreement," the Islamist number two said.
He said he had told the ruling party that the Popular Congress was willing to take part in a committee that is to draft a new constitution "if the government and SPLM agree on a reasonable representation of the political forces in it."
Ahmed said he had reiterated his party's demand for the swift establishment of the broad-based government stipulated by the peace agreement with the SPLM, but was otherwise far less outspoken in his criticism of the government than recent statements from his party.
A statement released by the Popular Congress after the adoption of a UN Security Council resolution last week requiring the surrender of senior officials for trial on war crimes charges in The Hague said the regime's continued existence had "become a major threat to the country."
It demanded the lifting of the longstanding state of emergency and the release of all political prisoners as well as respect for political and personal freedoms.
But almost alone among opposition parties, the Popular Congress backs the government's defiance of Resolution 1593 and its demand for trials before the International Criminal Court of officials accused of war crimes during the suppression of a two-year-old ethnic minority uprising in Darfur.
"We are for the country's sovereignty and independence," said Ahmed.