Israel says its jets have hit two targets in the Gaza Strip.

The Israeli military said the targets were Hamas weapon manufacturing facilities, adding that the strikes were in response to two rockets fired from Gaza into southern Israel.

A pregnant woman and her young daughter in a nearby house were killed, Palestinian officials said.

In the West Bank, Israeli police say a Palestinian woman set off an explosive device at a checkpoint.

She was stopped by police while driving on Sunday morning near the Israeli settlement of Maale Adumim.

She "shouted 'Allahu Akbar' (God is great) and detonated an explosive device", a police spokeswoman said, adding that the woman was in critical condition and a policeman was slightly wounded.

Initial reports had said the woman had died in the blast.

"The IDF holds Hamas responsible for any act of aggression from the Gaza Strip," said Israel Defense Forces' spokesman Lt Col Peter Lerner in a statement following the air strikes early on Sunday.

As well as the two reported deaths, medical staff in the Zeitun sector south of Gaza City say three people are trapped in the rubble of the destroyed house.

There have been weeks of tension over access to a site in East Jerusalem sacred to both Jews and Muslims.

Palestinians fear Israel plans to change arrangements at the al-Aqsa mosque/Temple Mount compound, where Jews are allowed to visit but not allowed to pray - something Israel insists it will continue.

There have been fierce protests in the West Bank. Photo: AP

Earlier, US Secretary of State John Kerry expressed "deep concern" over the situation.

He made separate phone calls to Israeli PM Benjamin Netanyahu and Palestinian Authority President Mahmoud Abbas.

In his phone calls earlier  Kerry "stressed the importance of upholding the status quo in word and deed" at the site, the state department said.

He offered his support in efforts to restore calm, but both men blamed the other side for the rising violence.

Netanyahu "made it clear that he expects the PA [Palestinian Authority] to stop its wild and mendacious incitement, which is causing the current wave of terrorism", his Twitter account said.

 Abbas told  Kerry that Israel should stop settler “provocations”, which he said were carried out under Israeli army protection, his office said.

In other developments on Saturday:

-- Netanyahu ordered the mobilisation of hundreds of police reservists to restore security

--Israeli police shot dead two Palestinian youths during clashes close to the border with the Gaza Strip

--Four Israelis were hurt in two separate stabbings - both Palestinians assailants were shot dead by Israeli troops

--Violent protests broke out after the funeral of a Palestinian man who had been shot during unrest at the Shuafat refugee camp in East Jerusalem and later died of his injuries.

The violence has spurred talk from Hamas, which dominates Gaza, of a new Palestinian intifada, or uprising.

But the clashes have not yet reached the scale of previous intifadas, with no clear mass movement or leadership so far emerging.