Israeli military claimed it struck 25 more Hamas sites overnight, bringing the total to more than 60 targets in the Gaza Strip over 24 hours.
The exchange of fire has raised fears over another war in the beleaguered Palestinian enclave, which would be the fourth since 2008.
Israel said the airstrikes were in response to some 70 rockets and mortars fired into the territory throughout the day Tuesday, a number of which were intercepted by the air defence system.
Three Israeli soldiers were wounded, the military said. There were no immediate reports of casualties in Gaza.
Palestinian claims of a ceasefire followed Tuesday's flare-up as explosions continued into the night. Late Tuesday, an Islamic Jihad spokesperson said a ceasefire agreement had been reached.
Senior Hamas official Khalil al-Hayya similarly said on Wednesday that an accord had been reached over the violence in Gaza.
In a statement, al-Hayya said, "a number of mediators intervened in the past hours and an agreement was reached to return to a ceasefire in Gaza", adding that the group was committed to it as long as Israel was.
Israel's Intelligence Minister Yisrael Katz, however, denied talk of a deal.
"Israel does not want the situation to deteriorate, but those who started the violence must stop it," he said on Israeli public radio.
"Israel will make (Hamas) pay for all its fire against Israel."
In a rare joint statement, both Hamas and Islamic Jihad claimed shared responsibility over the rocket and mortar fire, saying it was in retaliation for Israeli attacks targeting their positions.
Three Islamic Jihad members were killed in an Israeli strike Sunday, and the group has vowed revenge.
Tuesday's incidents follow weeks of deadly demonstrations and clashes along the Gaza border, beginning 30 March.
The protests, dubbed "the Great Return March", called for the right of return of refugees, and peaked on 14 May with the US decision to open its embassy in the contested capital Jerusalem.
Over 61 Palestinians were killed and 2,400 injured as tens of thousands protested along the besieged strip's border while snipers fired live ammunition and tear gas into the protesters.