Israeli airstrikes killed "two militants of the Islamic Jihad group" in Gaza on Wednesday as rocket fire toward Israel resumed after a brief overnight lull, raising the death toll in Gaza to 12 Palestinians in the heaviest round of fighting in months.

The Israeli military said more than 250 rockets have been fired at Israeli communities since the violence erupted after an Israeli airstrike killed a senior Islamic Jihad commander accused of being the mastermind of recent attacks.

Schools remained closed in Israeli communities near the Gaza border as rockets continued to rain down, albeit in lesser ferocity that during the relentless barrage the previous day.

But in a sign that the current round could be brief, Gaza's Hamas rulers have yet to enter the fray. Although larger and more powerful than the Iranian-backed Islamic Jihad, Hamas is also more pragmatic. With Gaza's economy in tatters, it appears to have little desire for another round of fighting with Israel.

Egypt, which frequently mediates between Israel and Gaza militants, has been working to de-escalate tensions, according to officials in Cairo.

Seeking to keep the outburst under control, the Israeli military has restricted its operations to Islamic Jihad, and nearly all the casualties so far are members of the militant group.

Tuesday's pre-dawn Israeli strike came almost simultaneously as another strike attributed to Israel, which targeted a senior Islamic Jihad commander based in Syria. The strikes appeared to be a new surge in the open warfare between Israel and Iranian proxies in the region.

Iran has forces based in Syria, Israel's northern neighbour, and is accused of supporting Hezbollah militants in Lebanon. In Gaza, it allegedly supplies the Islamic Jihad group with cash, weapons and expertise. Israeli Prime Minister Benjamin Netanyahu has also claimed that Iran is using Iraq and far-off Yemen, where Tehran allegedly backs the Houthi rebels in war with a Saudi-led coalition backing the government, to plan attacks against Israel. Hamas also receives some support from Iran.

Israel frequently strikes Iranian interests in Syria but Tuesday's attack in Damascus appeared to be a rare assassination attempt of a Palestinian militant in the Syrian capital.