Israeli air strikes on Gaza killed one Palestinian and wounded eight on Wednesday, the Palestinian Health Ministry in the besieged enclave said.
The Israeli army said Hamas launched about 70 rockets into Israel, most of which were intercepted by the Iron Dome aerial defence system or fell in open areas. Three Israelis sustained minor injuries from the attacks.
The rockets followed confrontations between Hamas fighters and Israeli forces earlier on Wednesday, in which Israel said it had shelled a Hamas post after Palestinian gunfire struck an engineering vehicle along the Gaza fence.
The Health Ministry identified Wednesday's victim as 30-year-old Ali al-Ghandour.
On Tuesday, two Palestinians were killed in an Israeli raid on Gaza.
However, Palestinians and Israelis are now in "advanced stages" of indirect negotiations to defuse tensions, a Hamas official was cited as saying.
Neither Hamas nor Israel, which last fought a war in 2014, appears keen on another full-blown conflict. But public demands by both sides for detainee releases appear to be a stumbling block in securing a long-term truce.
"We can say that actions led by the United Nations and Egypt are in advanced stages and we hope it could yield some good from them," Khalil Al-Hayya, deputy Hamas chief in Gaza, told al-Jazeera television.
"What is required is for calm to be restored along the border between us and the Zionist enemy."
Israel has played down prospects for a comprehensive ceasefire, speaking in terms of a more limited quid-pro-quo.
Israeli officials said on Sunday they would reopen a commercial border terminal and expand a Palestinian fishing zone.
Israeli Prime Minister Benjamin Netanyahu called off a trip to Colombia this week to attend to the Gaza truce talks, and was due to convene his decision-making security cabinet on Thursday to discuss the negotiations.
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Avi Dichter, head of the Israeli parliament's foreign affairs and defence committee, struck a cautiously upbeat note on Wednesday. "I very much hope that we are on the brink of a new day on the matter of Gaza," he told reporters.
Hayya said foreign donors were collecting "hundreds of millions of dollars" for electricity, water, health and job-creation projects in Gaza, but that these "require stability".
Despite talks of de-escalation, Hamas warned that it is prepared to fight back against Israeli attacks.
"Al-Qassam Brigades, Hamas armed wing, is ready and well-prepared to confront the aggression and defend its people," Issam Daalees, a senior Hamas leader, said in a statement. "The enemy must understand that it cant unilaterally impose the rules of confrontations and it must bear the consequences of its stupidity."
Israel wants to recover the bodies of two soldiers killed in the last Gaza war, and wants the release of two of its civilians who wandered into the enclave, in exchange for any far-ranging truce deal with Hamas.
For its part, Hamas demands that Israel free Palestinian prisoners.
"We want to free our brave prisoners and we have no objection to beginning now," Hayya said. "Let it be a prisoner swap deal, (Palestinian) prisoners in return for Zionist soldiers."