Another day passed today without the promised resignation of Prime Minister Menachem Begin, deepening the mystery surrounding Begin's condition.

The prime minister did not attend Sunday's Cabinet meeting and did not appear at his office today or yesterday. According to his aides, Begin is suffering from a cold and the flu but is working at home.

However, speculation continues over the state of health of the 70-year-old Begin, prompting his spokesman, Uri Porat, today to deny reports that the prime minister has stopped eating.

Begin announced Aug. 28 that he intended to resign and reaffirmed that decision two days later after rejecting pleas he remain in office. At the same time, Begin agreed to delay the legal step that would implement his decision--submission of a letter of resignation to President Chaim Herzog--to give his political allies time to designate a successor and prevent Herzog from asking the opposition Labor Alignment to try to form a new government.

That process appeared to have been completed last night when leaders of the current government coalition signed an agreement to continue under the leadership of Foreign Minister Yitzhak Shamir, chosen by Begin's political party as his successor. This led to anticipation that Begin would resign today.

According to a source close to Shamir, the signing of the new government coalition agreement apparently did not complete Shamir's tasks in preparing to succeed Begin. He said Shamir continued to hold political discussions with various allies today and has still not informed Begin that he is ready to form a new government.

After Begin resigns Herzog is obligated to consult with leaders of the parliament and to ask one of them to try to form a government.

The delay in Begin's resignation was designed to give Shamir time to line up a solid parliamentary majority in advance, leaving Herzog no choice but to turn to him.

Such a delay is not precluded by Israeli law, but it has led to criticism that Begin is seeking to circumvent the government succession process and more recently to renewed questions about the state of the prime minister's health.