RAMALLAH -  Palestinian president Mahmud Abbas will refuse to meet US Vice President Mike Pence later this month following Washington's controversial policy shift on Jerusalem, an Abbas aide said on Saturday, as protests gripped the Palestinian territories for a third straight day.

Retaliatory Israeli air strikes on the Gaza Strip killed two Hamas fighters before dawn, as unrest simmered over President Donald Trump's recognition of Jerusalem as Israel's capital on Wednesday.

Four people have been killed and dozens wounded since Trump announced the move, which drew criticism from every other member of the UN Security Council at an emergency meeting on Friday.

"There will be no meeting with the vice president of America in Palestine," Abbas's diplomatic adviser Majdi al-Khaldi told AFP. "The United States has crossed all the red lines with the Jerusalem decision," he added.

Egypt's Coptic Pope Tawadros II also cancelled a meeting with Pence, with the church saying it "declines to receive" him in protest at Trump's announcement which failed to take into account the "feelings of millions" of Arabs.

That decision came a day after Ahmed al-Tayeb who heads Al-Azhar, Egypt's top Sunni Muslim institution, also scrapped plans to meet the US vice president over the "unjust and unfair American decision on Jerusalem".

There were fresh clashes on Saturday as Palestinian protesters in the occupied West Bank hurled stones at Israeli troops who responded with tear gas, rubber bullets and live rounds.

In the Gaza Strip, mourners vented their anger at the funerals of two people killed during clashes at the border fence on Friday and the two Hamas militants killed early on Saturday.

Later Saturday unrest spread into Israel when a bus was stoned as it passed near Arab towns in the northern Wadi Ara district, injuring the driver.

Police said they arrested two young men from the Israeli Arab town of Arara.

An Israeli army statement said "violent riots have erupted at approximately 20 locations" in the West Bank and the Gaza Strip, with protesters throwing rocks, petrol bombs and rolling burning tyres at troops.

It said soldiers responded with unspecified "riot dispersal means", lightly wounding three Palestinians.

In Israeli-annexed east Jerusalem, police fired stun grenades to disperse Palestinian demonstrators on the main Salahedin Street, an AFP cameraman said.

A police statement said four policemen were slightly injured and 13 protesters arrested.

The Palestinian Red Crescent said 12 Palestinians were injured by shrapnel from grenades or by blows from police.

There have been fears of a much larger escalation of violence after Hamas leader Ismail Haniya called for a new Palestinian intifada, or uprising. Hamas and the smaller Islamic Jihad militant group both renewed that call on Saturday.

Dozens of protesters were wounded by rubber bullets or live fire in clashes in the occupied West Bank, the Gaza Strip and Jerusalem that followed the main weekly Muslim prayers on Friday. Tens of thousands also protested in Muslim and Arab countries, including Jordan, Turkey, Pakistan and Malaysia.

Saturday's pre-dawn air strike on a base of Hamas's military wing in Nusseirat, in the central Gaza Strip, was one of several, the Israeli military said.

A statement said the air force "targeted four facilities belonging to the Hamas terror organisation" in Gaza a day after three rocket attacks from the Palestinian enclave into southern Israel.

One rocket hit the southern Israeli town of Sderot, although public radio said it did not explode and did not cause any casualties. Israel had already responded on Friday night to the first two rockets with air strikes in which the Gaza health ministry said 14 people were wounded, among them women and children.

In an Arabic-language Facebook post on Saturday, a senior Israeli military officer warned the people of Gaza. "Continued fire will result in a harsh and painful response from the Israel Defence Forces, so do not test our strength," wrote Major General Yoav Mordechai, head of the defence ministry agency responsible for civilian affairs in the Palestinian territories.

The Hamas health ministry in Gaza said the two men killed in Saturday's strikes were members of the movement's armed wing, which has fought three wars with Israel since 2008.

Trump's decision drew lavish praise from Israeli Prime Minister Benjamin Netanyahu but has sparked a worldwide diplomatic backlash.

Five European countries on the Security Council insisted the new US policy was inconsistent with past resolutions, including one that declares east Jerusalem to be Israeli-occupied.

The meeting was requested by eight of the council's 15 members but was largely symbolic as no vote on a resolution was planned because the US wields veto power.

Trump said his defiant move - making good on a 2016 presidential campaign pledge - marked the start of a "new approach" to solving the Israeli-Palestinian conflict.

The decision is likely to impact domestic Palestinian politics, particularly between Abbas's Fatah and the Islamist Hamas, now at a key stage in a fragile reconciliation process after a decade of bitter enmity.

Abbas "will soon take a harder line toward the peace process and a softer line toward Hamas than he otherwise would have," wrote Ghaith al-Omari of the Washington Institute of Near East Policy.

Hamas, which violently seized Gaza from Fatah in 2017, is due to formally hand back power on Sunday.

Hamas spokesman Fawzi Barhum said in a statement on Saturday the group "reiterated its commitment to all that has been signed and agreed upon and the completion of the handover".