Palestinians have held demonstrations across the region to protest President Donald Trump’s Middle East initiative, while militants in the Gaza Strip fired rockets and mortar rounds at Israel, drawing retaliatory strikes.

The Palestinians have rejected the Trump plan, which heavily favours Israel and would allow it to annex all of its Jewish settlements, along with the Jordan Valley, in the occupied West Bank. The Palestinians were offered limited self-rule in Gaza, parts of the West Bank and some sparsely populated areas of Israel in return for meeting a long list of conditions.

Israel launched airstrikes on militant targets in Gaza early Friday, shortly after Palestinians fired three rockets into Israel, two of which were intercepted, the military said.

It said that Palestinian militants had also launched “explosive balloons” toward Israel and that a sniper had shot an observation antenna. The military said it struck targets linked to the Hamas militant group in response, including “underground infrastructure used to manufacture weapons.”

Throughout the day, Gaza militants fired several rounds of mortars and projectiles. An Israeli tank fired on a Hamas military post, and Israeli aircraft struck additional militant sites in Gaza early Saturday.

No one was wounded in either exchange of fire, but an Israeli woman dropped her three-week-old baby while running into a bomb shelter during the rocket attack, according to the United Hatzalah rescue service. The baby was hospitalised and is in moderate condition.

Gaza has been relatively calm in recent months as Egyptian and UN mediators have worked to shore up an informal truce between Israel and Hamas, which rules the coastal territory.

Hamas has curbed rocket fire and rolled back weekly protests along the frontier that had often turned violent. In return, Israel has eased the blockade it imposed on Gaza after the Islamic militant group seized power from forces loyal to the Palestinian Authority in 2007.

Hamas rejected the Trump plan and vowed that “all options are open” in responding to the proposal, but the group is not believed to be seeking another war with Israel.

The plan anticipates $US50 billion ($A75 billion) of investment in the future Palestinian state and describes several ambitious development projects, without saying where the money would come from.

Palestinians in the West Bank and Gaza have held small, scattered protests in recent days condemning the Trump initiative, and thousands gathered in Gaza on Friday, where they burned US and Israeli flags and portraits of Trump and Israeli Prime Minister Benjamin Netanyahu.

At least 14 Palestinians were wounded by Israeli gunfire in scattered protests along the security fence surrounding Gaza, according to the Palestinian Red Crescent medical service.

-AAP