Defence Minister Avigdor Lieberman, who said he opposed ending the strikes on Gaza, scheduled an early afternoon press conference as rumours swirled that he would resign.
The agreement also led to protests by several hundred Israelis living near the border with Gaza who called for further action against its rulers Hamas.
Prime Minister Benjamin Netanyahu did not comment in detail on the agreement, but defended his strategy and said: "Our enemies begged for a ceasefire.
"In times of emergency, when making decisions crucial to security, the public can't always be privy to the considerations that must be hidden from the enemy," he said at a ceremony on Wednesday morning in honour of Israel's founding father David Ben-Gurion.
Hamas portrayed the ceasefire as a victory and thousands of residents of the blockaded enclave took to the streets late Tuesday to celebrate.
"The resistance has defended itself and defended its people against Israeli aggression," Hamas leader Ismail Haniya said.
Hamas announces ceasefire with Israel after worst escalation in years
The Egyptian-brokered truce was announced by Gaza militant groups, including Hamas, on Tuesday.
Hamas said it would abide by the deal, which the UN also helped broker, as long as Israel did the same.
A diplomatic source familiar with the agreement said it involved returning to arrangements put in place following the 2014 war, but warned: "The situation remains very precarious and can blow up again.
"What we have seen in the past 48 hours was very dangerous and no efforts should be spared to avoid similar flare-ups."
The violence saw seven Gazans killed in 24 hours as Israeli strikes targeted militants and flattened buildings, sending fireballs and plumes of smoke into the sky.
Sirens wailed in southern Israel as militants unleashed barrages of rocket and mortar fire, sending residents rushing to shelters.
Around 460 rockets and mortar rounds were fired at Israel, the most ever in such a brief time period, the army said.
An anti-tank missile hit a bus near the Gaza border that Hamas says was being used by Israel's army. An Israeli soldier was severely wounded.
In all, some 27 Israelis were wounded, three of them severely.
A Palestinian labourer from the occupied West Bank was killed when a rocket hit a building in the Israeli city of Ashkelon.
The violence began on Sunday with a botched Israeli special forces operation inside the Gaza Strip that turned deadly and prompted Hamas to vow revenge.
The clash that resulted from the blown operation killed seven Palestinian militants, including a local Hamas military commander, as well as an Israeli army officer.
UN Security Council meets on Gaza violence
Militants responded with the rocket barrages and an anti-tank missile, prompting Israeli air strikes across Gaza.
The Israeli army said it struck some 160 targets, including Hamas's Al-Aqsa TV station and internal security headquarters in Gaza City.
At least five of the dead in Gaza were claimed as members of various militant groups. Some 26 people were wounded, according to territory's health ministry.
The escalation came despite Netanyahu's decision to allow Qatar to transfer millions of dollars in aid to Gaza for salaries as well as fuel to ease a chronic electricity shortage.
The agreements had led to calmer protests along the border after months of deadly unrest.
Sunday's special forces operation and resulting clash upset those efforts, leading to questions over the timing of the covert Israeli move.
Israel said it was an intelligence-gathering operation and that those efforts must continue to defend the country.
Israel and Palestinian militants in Gaza have fought three wars since 2008, and protests and clashes along the Gaza border since March 30 have repeatedly raised fears of a fourth.
At least 234 Palestinians in Gaza have since been killed by Israeli fire, the majority during protests and clashes.
Two Israeli soldiers have been killed over the same period.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ