In his first public comments on the deal, Abdel Fattah al-Burhan said he had consulted the prime minister and most political forces before the agreement was announced on Friday in a call with US President Donald Trump and Israeli Prime Minister Benjamin Netanyahu.
The move is controversial in Sudan, once a staunch enemy of Israel, and has stirred opposition from some prominent political factions.
"I always prefer to call it reconciliation instead of normalization," Burhan said in a televised interview. "So far, we have not concluded an agreement. We will sign with the other two parties, America and Israel, on the aspects of cooperation."
Burhan leads a military-civilian sovereign council that took charge after the ouster of former president Omar al-Bashir last year following popular protests.
A government of technocrats has been grappling with an economic crisis that includes rapid inflation, a weakening currency, and shortages of essential goods.
Sudan won the prospect of some relief last week when the United States confirmed it would lift Khartoum from its list of state sponsors of terrorism, a designation that had blocked international funding and debt relief.
Many Sudanese saw the move as unduly delayed and deployed to pressure Sudan into accepting the deal on Israel.
"We were not subjected to blackmail," said Burhan. "We lay down our interests and we found benefits, and it could be that we gain more than the other parties."Burhan said tense relations with the civilian component of the sovereign council had improved recently, and that he had agreed with civilian political leaders that the deal on Israel should be approved by a yet-to-be formed legislative council.