Palestinians have carried out three stabbing attacks against Israelis and police in Jerusalem, with two of the attackers shot dead, Israeli police said.

Two Palestinians stabbed two Israelis in Jerusalem, prompting police to open fire, killing one of the attackers and wounding the other, police spokesman Micky Rosenfeld said.

Police said the two victims, one aged 16 and the other 20, were seriously wounded in the attack in Pisgat Zeev, a Jewish settlement in traditionally Arab east Jerusalem.

Earlier on Monday, elsewhere in Jerusalem, police officers noticed a Palestinian man acting suspiciously and ordered him to take his hand out of his pocket, Israeli police spokeswoman Luba Samri said.

The man then attacked an officer with a knife, but the officer was wearing a protective vest and was not injured, she said. Other officers shot the attacker dead, police said.

The attack took place near the Lions Gate of Jerusalem's walled Old City on the predominantly Arab eastern sector.

In the afternoon, an Israeli police officer confronted a Palestinian woman who was acting suspiciously, Ms Samri said. The woman then stabbed and lightly wounded him before he shot and wounded her, she said.

That attack took place near police headquarters in Jerusalem, in an area that straddles the eastern district and the predominantly Jewish west.

Recent days have seen a series of stabbing attacks in Israel and the West Bank that have wounded several Israelis. Nine of the attackers have been shot dead.

Past weeks have also seen violent demonstrations in the West Bank and Gaza, and at least 16 Palestinians have been killed by Israeli forces, including a mother and toddler killed on Sunday in a Gaza air strike.

At the start of the month, two Israelis were killed in a West Bank shooting attack and two Israelis were stabbed to death in Jerusalem. Last month an Israeli motorist was killed when Palestinians hurled stones at his vehicle in Jerusalem, causing it to crash.

Israeli prime minister Benjamin Netanyahu has blamed the violence on incitement by groups including the Islamic Movement, which runs religious and educational services for Arab citizens of Israel. Mr Netanyahu is seeking sanctions on the group, which has led a campaign accusing Israel of plotting to take over a sacred Old City compound revered by both Jews and Muslims, a claim Israel denies.

Israeli police said they have arrested a local leader of the Islamic Movement in the Bedouin Arab town of Rahat in southern Israel who was suspected of organising a group of protesters who vandalised security cameras and other property in the town on Friday, as demonstrations have been taking place in predominantly Arab cities throughout Israel.

The European Union's top diplomat, foreign policy chief Federica Mogherini, told Mr Netanyahu and Palestinian president Mahmoud Abbas in phone calls on Sunday evening to avoid action that could increase tensions, and called on both sides to agree on "substantial steps which would improve the situation on the ground" and lead to renewed peace talks, according to an EU statement.

Marwan Barghouti, a popular Palestinian figure who was convicted of planning deadly attacks on Israelis during the second intifada, published a piece in The Guardian newspaper on Sunday saying the cause of recent violence was "denial of Palestinian freedom".

Barghouti, who was arrested in 2002 and is serving five life sentences, is seen as a possible successor to Mr Abbas.

Mr Netanyahu lashed out at Arab politicians in the Israeli parliament, accusing them of participating in what he says is incitement fuelling the wave of unrest sweeping the country.

In an address to parliament, Mr Netanyahu accused Arab parties of "undermining" the country, saying that certain politicians have spoken in favour of violence against Israelis.

He called on Israel's Arab citizens to "kick out the extremists among you".

Israel's Arab minority has full citizenship rights, but often suffers discrimination. Mr Netanyahu, who just a few months ago warned his supporters that Arabs were voting in large numbers on election day, said he was committed to coexistence.

Mr Netanyahu also said Palestinian accusations that Israel is plotting to take over a sensitive Jerusalem holy site are an "absolute lie".

Mr Netanyahu dismissed the claims as "incitement" and said the series of stabbings of Israelis "stems from the desire to annihilate us".

He called on Mr Abbas to condemn the violence.