Private sources told Al-Jazeera that there is no final offer of truce until this moment, and contacts are continuing between all parties.
This comes after the Associated Press quoted Israeli officials who told US officials that the operations could end within days.
Israeli media also reported that Egypt had submitted a proposal for a ceasefire as of next Thursday morning.
The Security Council, in 3 recent sessions, failed to come up with a declaration calling for an end to the aggression on Gaza (Anatolia)
Disappointment
In the context of efforts to stop the Israeli aggression on Gaza, the Arab group at the United Nations expressed its "disappointment" at the failure of the Security Council to move to stop the Israeli aggression on the Gaza Strip.
This came in a joint press conference held by the Algerian ambassador to the United Nations, Sofiane Mimouni, whose country holds the presidency of the group this month, with Ambassador Riyad Mansour, Palestine Observer of the International Organization, which is based in New York.
Mimouni said that Algeria requested an urgent meeting of the United Nations General Assembly on the latest developments in Palestine next Thursday.
He expressed the Arab group’s disappointment at the Security Council’s failure to deal with the dangerous situation on the ground in Gaza, and its reluctance to demand the occupying power to stop its aggression.
For his part, Mansour stressed that stopping the occupation crimes against the Palestinians in Gaza and Jerusalem requires the strong will and determination of the international community to stop them.
Tonight, behind closed doors, the Security Council holds its fourth session on the situation between Israel and the Palestinians.
During three council sessions in the past few days, the United States - an ally of Israel - prevented a consensus on issuing a statement calling for an immediate cessation of the fighting.
The issuance of council statements requires the unanimous approval of all of its 15 member states.
Earlier, US Secretary of State Anthony Blinken held two phone calls today, with his Bahraini and Moroccan counterparts, to discuss developments in the Gaza Strip, the West Bank and Israel.
This came according to two US State Department statements. The first statement mentioned that Blinken spoke with his Bahraini counterpart, Abdul Latif Al Zayani, about efforts to stop the Israeli-Palestinian conflict.
The US State Department stated - in a second statement - that Blinken and his Moroccan counterpart Nasser Bourita expressed their concern about the ongoing violence in the Middle East, which has claimed the lives of civilians on both sides.
For her part, the American delegate to the United Nations expressed her lack of belief that the issuance of a declaration by the Security Council at the present time would help in de-escalation.
She added that Washington did not remain silent, but rather was and is still making diplomatic efforts to stop the violence by communicating with leaders in the Middle East.
Merkel called for an urgent ceasefire and the launch of political negotiations (Deutsche Welle)
A German-Jordanian call
As part of the efforts to stop the Israeli aggression on Gaza, German Chancellor Angela Merkel and King Abdullah of Jordan called today, Tuesday, for an "immediate ceasefire" as a result of the Israeli aggression on Gaza.
This came during a phone call between the two leaders.
A German government statement said that Merkel and the King of Jordan agreed that initiatives should be supported in order to establish a rapid ceasefire to provide conditions for the resumption of political negotiations.
According to the Jordanian royal court’s statement, King Abdullah said - during the call - that the tragic developments in the Palestinian territories were the result of repeated Israeli violations against the Palestinian people.
"Preventing the recurrence of the Israeli escalation and stopping the cycle of violence requires finding a political solution to the Palestinian issue that leads to a just and comprehensive peace based on the two-state solution," he added.
He stressed the importance of the international community’s role in stopping the "serious and repeated" Israeli violence and attacks that led to this escalation.
The Minister of Foreign Affairs of Jordan also discussed with his Greek counterpart, today, Tuesday, developments in the Palestinian territories and the efforts made to push for international action capable of stopping the aggression.
This came during a meeting between the Jordanian foreign ministers, Ayman Safadi and the Greek, Nikos Dendias, as part of an official visit by the Greek minister to the Kingdom.
According to a statement by the Jordanian Ministry of Foreign Affairs, the two ministers stressed that there is no alternative to the two-state solution in accordance with international law and international references adopted in order to achieve peace and resolve the conflict.
Safadi stressed that achieving a just and comprehensive peace cannot be achieved unless the Palestinian people obtain their legitimate rights in full.
European Union
Earlier on Tuesday, the European Union’s foreign policy chief, Josep Borrell, said that the priority now is for a ceasefire between the Palestinians and Israel, and for the delivery of humanitarian aid to the Gaza Strip.
Borrell’s statement came during a press conference held in Brussels this evening, after an emergency telephone meeting with the foreign ministers of member states, which focused on discussing the current crisis in the Middle East.
United Nations Secretary-General António Guterres also called on the Security Council to take a "unified position" to stop the fighting.
This was stated by Stefan Dujarric, spokesman for the Secretary-General, during a press conference at the United Nations headquarters in New York.