Islamic Jihad leader Zeyad al-Nakhala said a truce could be agreed immediately if Israel accepted the Iranian-backed faction's terms.
Palestinian militant group Islamic Jihad offered terms on Wednesday for an Egyptian-mediated ceasefire with Israel, saying if these were not met it was prepared to keep up cross-border rocket attacks indefinitely despite a mounting Gaza death toll.
The worst surge in fighting around the Palestinian enclave was sparked on Tuesday when Israel killed Islamic Jihad's top Gaza field commander in an airstrike, accusing him of masterminding a spree of recent attacks and planning more soon.
As Islamic Jihad fighters responded with hundreds of rocket launches that reached as far as Tel Aviv and paralysed parts of Israel, it pressed the aerial barrage on the Gaza Strip.
Medics say 26 Palestinians, including at least 14 gunmen and six civilians, have been killed. Dozens have been injured on both sides.
In his first public comments on the fighting, Islamic Jihad leader Zeyad al-Nakhala said a truce could be agreed immediately if Israel accepted the Iranian-backed faction's terms.
These included Israel ending targeted killings of militants, its sometimes lethal response to weekly Gaza protests and steps to ease its blockade on the coastal Palestinian enclave, al-Nakhala, who is based in Beirut, told Al-Mayadeen TV.
Al-Nakhala said he expected to hear Israel's response via Cairo within hours. Should a truce not be agreed, he said, "the (Islamic Jihad armed wing) Jerusalem Brigades is able to manage the battle, and for a long time".
Israel signalled openness only to a quid-pro-quo restraint.
"Quiet will be answered with quiet," Israel's Army Radio quoted an unnamed Israeli government official as saying. "Islamic Jihad wants a ceasefire, and it is thus trying to create a false impression of achievements."
Israel had previously said it sought no escalation in Gaza. Unlike with past rounds of fighting, when Israel held Gaza's dominant Hamas faction responsible for any cross-border attacks, this time Hamas has been spared Israeli retaliation.
Hamas, in turn, has voiced solidarity with Islamic Jihad but has not claimed responsibility for any of the rocket launches.