(CNN) Violence has once again broken out near Jerusalem's Damascus Gate Plaza, where police on Wednesday shot and killed a man dressed in combat fatigues and armed with a knife.

Initially, Israeli police said an attacker tried to stab a private bodyguard protecting a family visiting Jerusalem's Old City. A short time later, police spokeswoman Luba Samri said the incident began when border police saw a man who seemed nervous and suspicious.

As officers approached him, Samri said, the man allegedly lunged at them with a knife. The man then ran toward another police unit, members of which yelled out, "He's a terrorist," before they fatally shot him, Samri said.

The Israel Security Agency identified the perpetrator as Basel Sider, 19, of the West Bank city of Hebron. He had no record, the agency said.

The incident was another violent episode near the gates of the Old City, sacred to three world religions.

Israeli police last Saturday killed two Palestinians who stabbed officers and others, authorities said. A 16-year-old Palestinian boy stabbed two Israelis about 150 yards from the entrance, police said.

The victims, 62 and 65, were lightly injured; police killed the attacker after he allegedly ran toward officers with the knife, authorities said. The assailant was identified as Ishak Badran of Jerusalem.

Some experts on the Middle East have theorized that young people are being radicalized online and are acting as so-called lone wolves.

These random, unpredictable attacks have stumped Israeli police, Ben Wedeman reported Wednesday at the Damascus Gate. Authorities cannot seem to come up with any link between these attackers and organized groups such as Hamas or Fatah, or Islamic Jihad, he said, and it's difficult to devise a streamlined strategy to fight them.

Israeli Prime Minister Benjamin Netanyahu had already ordered police reinforcements in Jerusalem, according to his office. About 1,300 reserve border police officers were dispatched there and nearby.

In more violence Wednesday, a 72-year-old woman was stabbed near Jerusalem's central bus station, Samri told CNN. A police officer shot the attacker.

The nationality of the victim and the attacker are unclear as police continue to investigate, Samri said. The woman is being treated at a hospital, police told CNN. Authorities have not released the condition of the attacker.

Abbas blames Israel

On Wednesday, Palestinian President Mahmoud Abbas struck a defiant tone as he addressed residents in a televised speech.

He assigned blame to Israel for committing what he called "extrajudicial executions."

Abbas said that peace and security would never exist in the region until a Palestinian state was established and warned of Israeli plots to undermine Palestinian objectives.

"Peace and security will never be achieved unless there is an end to the Israeli occupation and the establishment of an independent Palestinian state with Jerusalem as its capital," Abbas said.

"I hereby call on you, Palestinian people wherever you are, to stand together, to close ranks and be alert, to be aware of the Israeli plots to undermine our national mission," he said.

Abbas warned that Palestinians "will not be tied by agreements that are no longer respected by Israel and will continue to join international organizations and treaties."

He said that new files would be submitted to the International Criminal Court about what he called "extrajudicial executions carried out against our sons and daughters and grandchildren."

"He who is afraid of international law should stop committing crimes against our people," he said.

Checkpoints at some Palestinian neighborhoods

Abbas' statement comes on the same day that Israeli forces shut down access to some Palestinian neighborhoods in East Jerusalem by setting up checkpoints and putting more police on the streets, a reaction to a spike in violence across Israel and the Palestinian territories in recent days.

"These police actions and operations are intended to fairly respond to the wave of terror and knifing, within the framework of trying to return law and order to all citizens of the state," Samri said.

The moves came a day after U.S. Secretary of State John Kerry said he would travel to the Middle East to help calm the situation. It wasn't immediately clear when he planned to go.

Netanyahu pledged to make his nation more secure.

JUST WATCHED Netanyahu warns Palestinians over deadly attacks Replay More Videos ... MUST WATCH Netanyahu warns Palestinians over deadly attacks 01:05

"Today we ... decide on a series of vigorous steps in our fight against the sources of terrorism and incitement," Netanyahu said. "They will be implemented as quickly as possible."

In addition to cordoning off some Palestinian neighborhoods, Israeli authorities can demolish the homes of attackers, according to a statement from the Israeli government . There is a legal process that comes first, however, allowing homeowners to go before the Supreme Court of Israel. Forces cannot simply tear down homes without formal permission.

Military support

The military will back up the Israeli police force. An additional 300 more security guards will be recruited for duty on public transportation. Several recent attacks have taken place on buses or at bus stops.

"The Israeli police have heightened security over the last, in fact, 10 days. We've taken careful steps," spokesman Micky Rosenfeld told CNN's Wolf Blitzer on Wednesday. "Heightened security will continue."

He also said all the steps being taken "are being taken in order to make sure the situation stays under control and doesn't get out of hand."

Human Rights Watch condemned the new security measures.

"Locking down East Jerusalem neighborhoods will infringe upon the freedom of movement of all Palestinian residents rather than being a narrowly tailored response to a specific concern," said Sari Bashi of Human Rights Watch.

"The recent spate of attacks on Israeli civilians would present a challenge for any police force. But exacerbating the punitive policy of home demolitions is an unlawful and ill-considered response."

Bloody day

Israel's response followed a bloody day of attacks carried out by men that Israeli authorities say have ties to Palestinian terrorist groups.

At least three Israelis were killed, and many others wounded.

Two deaths came in an attack on a bus in Jerusalem's Armon Hanatziv, eliciting praise from Hamas, the militant group that controls Gaza.

"The Hamas movement blesses the heroic operations in Jerusalem," the group tweeted, "and hails the heroes who (carried them out)."

2 Israelis murdered in the 2 Terrorist attacks in Jerusalem. Police units patrolling areas to prevent attacks pic.twitter.com/kz5mvvc0f4 — Micky Rosenfeld (@MickyRosenfeld) October 13, 2015

The bodies of Palestinians killed in attacks on Israelis won't be returned to the families, the Israeli government said Wednesday.

"The families of the terrorists have turned their funerals into demonstrations of support for terror and incitement to kill and we should prevent this," said Gilad Erdan, Israel's public security minister. "We should do everything that terrorists will not get the honor and ceremony after the operations they carried out."

There was additional bloodshed in Haifa, where an Israeli Jew stabbed a man he mistakenly thought was Arab outside an IKEA. In another incident, an Israeli Arab was hit on the head with a stick on a beach in Netanya, according to Samri, the police spokeswoman.

There also was violence in Palestinian areas.

Clashes broke out between the Israel Defense Forces and Palestinians in Bethlehem in the West Bank after a Palestinian's funeral. The slain Palestinian was identified as Muataz Ibrahim Zawahra, 27. The Palestinian Ministry of Health said he was shot in the back Tuesday. The Palestinian Red Crescent and witnesses reported heavy fighting in Hebron, also in the West Bank.

The official Palestinian news agency, WAFA , reported at least five Palestinians were wounded Tuesday by "live ammunition" in northern Gaza at the Beit Hanoun crossing point. Eighteen were reportedly shot and injured the previous night at the Huwwara military checkpoint.

The Palestinian Red Crescent reported that 37 people were injured in Gaza. An additional 155 people received medical treatment in the West Bank and Jerusalem. Most had inhaled tear gas, but some were shot and beaten, the agency said.

The third intifada?

Some have suggested the widespread violence represents the start of the third intifada, or uprising, by Palestinians. But others have dismissed that assertion, saying the unrest is simply the consequence of the absence of any progress toward peace.

Whatever the label, some Palestinians insist they are fed up with the status quo.

"We've tried negotiations and it didn't work," a Palestinian youth in Hebron told CNN. "So now we will fight."

The Israeli government appears ready to fight back.

"Israel will settle accounts with the murderers, those who attempt murder and all those who assist them," Netanyahu said. "Not only will they not enjoy their privileges, but we will exact from them the full cost.

"Anyone who raises his hand to harm us -- will pay dearly. And we will not hesitate to use all means at our disposal to restore peace to the cities of Israel."