The new text "calls for the consideration of measures to guarantee the safety and protection of the Palestinian civilian population" in the occupied Palestinian territories and the Gaza Strip, according to the draft obtained by AFP news agency.
The Israeli military said more than 25 projectiles were fired on Tuesday.
"An agreement was reached to return to the (2014) ceasefire understandings in the Gaza Strip", Hamas' deputy chief in Gaza, Khalil al-Hayya, said. The IDF spokesman said the tunnel led from Gaza via Egypt to southern Israel, and that Hamas planned to use it to smuggle weapons from Egypt and to attack Israel.
"Palestinian factions will abide by calm as long as [Israel] abides by it", Islamic Jihad spokesman Daoud Shehab said.
At least seven Hamas and its allies bases were struck, security sources in Gaza said.
Amid worldwide condemnation of its use of lethal force at the mass demonstrations that began on March 30, Israel said numerous dead were militants and that the army was repelling attacks on the border fence.
Israel's military had not commented, but Intelligence Minister Yisrael Katz denied talk of a deal.
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Tuesday's exchange of fire came after weeks of deadly unrest along the fence between Israel and the blockaded Palestinian enclave. Egypt has also kept its crossing into Gaza closed for much of the past 10 years. Other residents reported machine- gun fire from Gaza.
The Hamas and the Palestinian Islamic Jihad announced Wednesday morning they reached a ceasefire agreement with Israel to return to Operation Protective Edge in 2014 outline. "There has still been no declaration of war, but the possibility exists".
"Indiscriminate attacks against civilians are completely unacceptable under any circumstances", she said. An Islamic Jihad spokesman said "the blood of our people is not cheap". He added that "of course, things could change". "I don't think serious people in Israel want to reoccupy Gaza", said Yaar.
This is the first time Hamas has claimed responsibility for shooting rockets at Israel since the 2014 war.
"This is something we can not tolerate", said Lt. Col. Jonathan Conricus, an Israeli army spokesman, who briefed journalists Tuesday.
The Israeli government did not reply to the Palestinian statements and released no official announcements regarding the ceasefire.
Islamic Jihad, an Iran-backed Palestinian terror organization, attacked southern Israel Tuesday morning by lobbing between 50 and 60 mortar shells at Israeli towns and communities in what is called the "Gaza belt".
France and Britain have criticised the draft resolution for a lack of specific details, diplomats said, adding the United States viewed it as biased against Israel.