Faisal Mohamed Saleh, the government spokesman, told the Sudan Tribune website that the cabinet had learned about the meeting through the media and ministers were not consulted beforehand.
He added that they would “wait for clarifications” when Gen Burhan returned from Uganda.
Monday’s announcement was denounced by other politicians and activists in Sudan.
Prime Minister Abdallah Hamdok, returning from a two-day visit to neighbouring Djibouti, made no comment — which the Tribune said was unusual.
But one of his predecessors Sadiq al-Mahdi said reconciliation with Israel did not “achieve Sudan’s national interest, nor does it achieve an Arab interest for us or a Palestinian interest.”
A statement from Mr Netanyahu’s office said on Monday that he believed Sudan was headed “in a new positive direction”.
It added: “Burhan is eager to help his country modernise by taking it out of isolation and putting it on the world’s map.”
US Secretary of State Mike Pompeo is understood to have contacted Gen Burhan to thank him for meeting Mr Netanyahu.
