Israel has launched several attacks on Gaza, killing at least 10 Palestinians and prompting Hamas to allege that the attacks violated an unofficial two-day-long truce.
An air strike on Rafah early on Wednesday, which killed Islamic Jihad member Ismail al-Ismar, sparked a flurry of retaliatory rocket attacks, followed by further Israeli raids.
The raids have killed at least 10 Palestinians and wounded 30 - many of whom were civilians.
On Thursday, Islamic Jihad said it would call off its rocket attacks if Israel first halted its air raids.
"If Israel stops its attacks, the Palestinian resistance will stop firing rockets," spokesman Daoud Shihab told AFP, saying the group did not want "an escalation".
A truce announced on Sunday night had been respected by resistance groups, including Islamic Jihad, until Israel chose to break it, he said.
"The last targeting in Rafah started the new crisis. Israel broke the truce when they killed one of the local leaders of the Al-Quds Brigades. After that, the Brigades answered this aggression," he said.
"The truce is related to Israeli action."
The renewed attacks raised fears of a fresh descent into violence scarcely 48 hours after factions had agreed to end rocket fire on southern Israel, on condition that the Israeli Air Force also stopped its raids.
Gaza's Hamas government accused Israel of violating the unwritten truce with its latest air strikes and called for UN intervention.
A statement issued by Hamas read: "Such aggressive behaviour confirms that Israel has no true intention of maintaining the truce and insists on escalating the situation. We call upon the international community and the United Nations in particular to pressure Israel to stop its aggression against our people."
Robert Serry, the UN's Middle East envoy who had worked with Egypt to set up Sunday's truce, expressed "deep concern" over the threat to the ceasefire and called on both sides to act immediately "to prevent any further escalation".
The latest cycle of violence erupted on Thursday, when gunmen attacked cars and buses on a desert road near the Red Sea resort town of Eilat, killing eight in an attack blamed on the Popular Resistance Committees.
In the following days, Israeli air strikes killed 15 Gazans, and armed factions in Gaza lobbed more than 100 rockets and mortar shells across the border, killing one man.
During the hunt for Thursday's attackers, Israeli troops shot dead an Egyptian army officer and four soldiers - causing a diplomatic rift between the two countries.
On Wednesday, Egyptian newspaper Al Masry Alyoum reported that Egyptian authorities have identified three of the people responsible for the attacks in Eliat. The report claims that the attackers were from the Sinai region of Egypt, not Gaza as Israel suspects.
The Israelis and Egyptians are currently conducting an investigation into the matter.