"We didn't know about the first attack until after the second one. They were in an area close to the border with Egypt, a remote area, desert, with no towns, no people."
His remarks were the first official government comments of the strikes, but the Sudanese transport minister had told Al Jazeera on Thursday that US aircraft had carried them out.
Mabrouk Mubarak Salim said that the attacks had been launched from the US fleet in the Red Sea.
The US military command in Africa (Africom) denied carrying out any attacks inside Sudan.
Israel has yet to comment on the claims.
Video footage supplied to Al Jazeera by a Sudanese intelligence source showed a number of burned-out and badly damaged vehicles lying in an expanse of desert.
Some media reports suggested that the raids had targeted arms smugglers destined for the Palestinian Hamas movement in the Gaza Strip.
But Sudan said there was no proof that the convoys were carrying weapons.
"They were smuggling something, but the pick-ups were small. You don't carry weapons in small pick-ups," al-Sadig said.
Hamas also denied that it was involved in the incident, saying that the fact that Sudan does not share a border with Gaza "shows these are false claims".
"First of all we are not sure any convoy has been hit, but it is ironic to link these convoys to Hamas," Salah al-Bardawil, a Hamas leader, told the AFP news agency.
"Should it turn out that there were raids and a high number of people killed, this would mean Israel is seeking to use the opportunity to blame Hamas and hit Sudan."
If the smugglers had been trying to get weapons to Gaza, they would have had to pass multiple Egyptian checkpoints both in the Nile valley and the Sinai peninsula.
Ronen Bergman, an Israeli investigative journalist, told Al Jazeera that weapons are smuggled to Gaza either from Syria by sea to the Sinai peninsula, or from Iran via Sudan.
"The last operation executed by the Israeli military forces in the Gaza Strip has caused Hamas to lose quite a lot of its arsenal and, therefore, to request for more and more supplies from Iran," Bergman said.
"Some of those supplies were intercepted in that alleged raid by the Israeli air force."
Israel staged a 22-day war in Gaza which ended when it declared a unilateral halt to military operations on January 18.