"Yesterday we were on the brink of war, and it has taken the concerted efforts of everyone to make sure that we step back from confrontation", Mladenov said in Gaza.
The prime minister promised to stop Hamas's bomb-laden kites and balloons during a surprise visit to the south. Twenty-five people were wounded across Gaza, the ministry said.
Israel's Beersheba court sentenced the Turkish Cooperation and Coordination Agency's (TIKA) representative in the blockaded Gaza Strip prisoner Mohammad Mortaji to nine years in prison.
Fuel deliveries will be suspended until Sunday, the military said in a statement.
"Nothing happens in Gaza without the consent of Hamas", said Gabi Siboni of Israel's Institute for National Security Studies think tank.
On Sunday, Israel said it discovered a falcon to which Gaza militants tied an incendiary device meant to set fires. Blasts from Israel's air strikes shook homes and shattered windows in Gaza, where plumes of smoke rose from the sites of the explosions.
Human rights groups have accused Israeli troops of using excessive force.
The defence ministry announced the move late Monday after saying last week it was closing the crossing to most deliveries, citing the kites and balloons that have for months carried firebombs into Israel from Gaza.
Hamas responded with more than 200 projectiles toward Israel communities, evoking memories of the three wars the sides have waged over the past decade.More news: Trump says he misspoke in Helsinki, expresses confidence in USA intelligence
Palestinians protesting along the Gaza border have begun attaching Molotov cocktails to kites to fly over the fence into Israel in a new tactic as demonstrations enter their sixth week.
Hamas called for the Israelis to re-evaluate their "calculations very well" before trying to change the "rules of engagement" with the Palestinian resistance. No Israelis have been killed.
Israeli Prime Minister Benjamin Netanyahu said Sunday at the start of the weekly Cabinet meeting that although rumours were circulating that the cease fire did not include a halt to the arson balloons and kites, "this is incorrect".
In an interview with Tasnim, Secretary of the Alliance of Palestinian Resistance Forces Khaled Abdul Majid said Egypt and Jordan are concerned about the American-initiated deal for ending conflicts in the occupied territories, saying the two countries cannot disclose the measures that the USA and Israel have urged them to take for implementing the deal.
Israel, the Hamas and Jihad groups had announced a ceasefire in Gaza, but Tel Aviv has kept its threat that the situation on the ground will determine whether it will hold.
No Israelis have been killed.
Israel says it is defending its sovereign border and accuses Hamas of using the protests as cover for attempts to breach the border fence and attack Israeli civilians and soldiers. In response, the IDF struck dozens of Hamas targets in the Strip.
"The strike was carried out in response to the fire terror being led by the Hamas terror organization against Israel's citizens and sovereignty", the IDF said in a statement.