A spokesman for UN Secretary-General Ban Ki-Moon has said that any violation of the ceasefire agreed today would be "utterly irresponsible".
He said the blockade of Gaza must end, and that the territory must be brought back under the control of one legitimate Palestinian government adhering to Palestine Liberation Organisation commitments.
"Israel's legitimate security concerns must be addressed," he added.
UN Secretary-General Ban Ki-moon has said he is deeply concerned at reports of a Russian aid convoy entering Ukraine without permission from the nation's government.
Ban's spokesman Stephane Dujarric said in a statement: "While recognizing the deteriorating humanitarian situation, any unilateral action has the potential of exacerbating an already dangerous situation in eastern Ukraine."
Pope Francis has urged the head of the United Nations to respond to the "heartfelt cries of despair of Christians and other religious minorities" in Iraq.
In a letter to Secretary General Ban Ki-Moon, he said:
I write to you, Mr Secretary General, and place before you the tears, the suffering and the heartfelt cries of despair of Christians and other religious minorities of the beloved land of Iraq.
The pontiff, who is on a visit to South Korea, has been commenting on the Iraq crisis on Twitter in recent days, and has called on Muslim religious leaders to condemn the actions of Islamic State militants.
United Nations Secretary-General Ban Ki-moon called on the Israeli and Hamas leaders to "show their humanity" and added that ending the Middle East conflict was "a matter of political will".
It's a matter of their political will. They have to show their humanity as leaders, both Israeli and Palestinian.
Why these leaders are making their people to be killed by others? It's not responsible, (it's) morally wrong.
The U.N. Secretary General Ban Ki-Moon has warned that Syria's announcement of plans for a presidential election will undermine attempts to find a political solution to the country's three-year-old civil war.
U.N. spokesman Stephane Dujarric said Ban Ki-Moon and Syria mediator Lakhdar Brahimi have "warned that the holding of elections in the current circumstances amid the ongoing conflict and massive displacement will damage the political process and hamper the prospects for a political solution."
He added: "Such elections are incompatible with the letter and spirit of the Geneva communique," referring to an agreement made in June 2012 on seeking a political transition in Syria.
UN Secretary-General Ban Ki-moon has voiced his alarm over the escalating Ukraine crisis in a phone call with Russian President Vladimir Putin.
"The Secretary-General ... underlined that any deepening of the crisis would be profoundly detrimental for all concerned; hence the need for everyone to work to de-escalate the situation," a statement from Ban's office read.
UN Secretary-General Ban Ki-moon said that he was "deeply concerned" by the situation involving Ukraine and Russia at a meeting with Russian President Vladimir Putin.
Ban is on a visit to both nations to encourage all parties involved in the crisis over Ukraine and its Crimea region, which Western nations say Russia has illegally annexed, to find a peaceful solution.
Russia's Foreign Minister Sergei Lavrov is set to meet UN Secretary-General Ban Ki-moon and UN diplomat Lakhdar Brahimi in Geneva later today, Reuters reported, citing Russian news agencies
Asked about the apparent gap in objectives between the two Syrian delegations, UN Secretary General Ban-Ki Moon said that the purpose of the talks is to "discuss how to implement the Geneva Communique" that was agreed in 2012.
This includes "establishing a transitional government," he said, adding that "everybody has come with the clear understanding that this is the basis" of the talks.
Today's session in the Syria peace talks has ended with UN chief Ban Ki-Moon calling on the Syrian delegations to work sincerely towards a solution.
A number of delegates at the conference are expected to give press conferences shortly.