Israelis stabbed in Tel Aviv, West Bank

• NEW: Israeli President calls for unity: "These are difficult days"


• A 20-year-old Israeli solider dies from his wounds


• Biden says he's Zionist; "Were there not an Israel," the U.S. "would have to invent one"


• Fatah accuses Hamas of bombing Fatah leaders' homes

(CNN) -- First, a 20-year-old Israeli soldier was stabbed Monday in Tel Aviv. Then, three Israelis were stabbed at a hitchhiking post near the entrance to a settlement in the West Bank, police said.

One of the three, a 24-year-old woman, was killed, emergency services said. The soldier stabbed earlier also died of his wounds, according to the Israel Defense Forces.

In both incidents, the attackers were "terrorists," police said.

"The atmosphere of violence rides the wave of Palestinian incitement," Israeli military spokesman Lt. Col. Peter Lerner said on Twitter.

The incidents came amid simmering tensions -- not just between Israel and Palestinians, but also between rival Palestinian factions Fatah and Hamas. Fatah controls the West Bank, while Hamas controls Gaza.

After the Tel Aviv stabbing, an 18-year-old Palestinian suspect from Nablus in the West Bank was arrested "with the help of eyewitnesses while he was hiding in an apartment building in the fourth floor nearby the central bus station," police spokeswoman Luba Samri said.

After the stabbings at the Alon Shvut junction in the West Bank, the attacker was shot by a security guard, police said.

The junction is the same site where three Israeli teens were kidnapped and later found dead, ultimately sparking an Israeli military campaign targeting Hamas in Gaza called Operation Protective Edge.

On Saturday, Israeli police shot and killed a Palestinian man who attacked police officers with a knife in a village in northern Israel, police said. The man killed was identified as Khair Hamdan. There were conflicting accounts of exactly what happened.

"These are difficult days," Israeli President Reuven Rivlin said about the stabbing Monday.

"I call on all elected officials, all our leaders, from all across the political spectrum, to stand united before the State of Israel. I place my trust in the security forces, that they will not rest until they return normality to our daily lives," he said.

Israel has faced stabbings from Palestinian terrorists before.

Last decade, Palestinian bus bombings and suicide attacks terrorized the country. The construction of the West Bank barrier has helped stave off some would-be bombers, while cutting off access to Jerusalem for many Palestinians.

The 'auto intifada'

Israel has been facing what some call an "auto intifada" -- a spate of attacks on Jewish civilians in Jerusalem by Palestinians driving vehicles.

Hamas said it "blesses the action. What is happening in Jerusalem is pushing us to prepare for war."

Violence recently has involved the Temple Mount, the holiest site in Judaism and one of the three holiest sites in Islam. It's known to Muslims as Haram al-Sharif, or the Noble Sanctuary, and Jews are allowed to visit the site but not to pray there.

A Palestinian recently shot and critically wounded a rabbi, Yehuda Glick, who campaigns for the right of Jews to pray at the site. After an Israeli counterterrorism unit shot and killed the assailant hours later, Palestinian Authority President Mahmoud Abbas -- part of Fatah in the West Bank -- wrote to the assailant's family saying he would "go to heaven as a martyr defending the rights of our people and its holy places."

The armed wing of the Palestinian militant group, Islamic Jihad, issued a statement Monday praising the stabbings, saying they "come as a natural response to the Zionists Occupation crimes in occupied Jerusalem, and the crime of assassinating in cold blood Khair Hamdan."

Fatah accuses Hamas of bombings

The incidents Monday -- the latest in a string of attacks -- came amid a new round of infighting between Palestinian factions.

The political party Fatah said Sunday it will scrap a series of events to commemorate the death 10 years ago of Palestinian leader Yasser Arafat. The group blamed rival faction Hamas, saying it is behind a series of bombings at the homes of Fatah leaders.

Hamas denounced the attacks, according to the Facebook page of spokesman Sami Abu Zuhri.

While the parties have fought violent battles in the past, they've made repeated announcements of plans to form a unity government as well.

Biden: I'm a Zionist

U.S. Vice President Joe Biden on Monday expressed U.S. solidarity with Israel.

"Were there not an Israel, the United States would have to invent one," he said in a speech to the Jewish Federation of North America. "It's more than merely a moral obligation we have, it's a security necessity. It's for both Israel's sake and the United States. The security of Israel and the United States is inextricably tied. And we will never, ever, ever abandon Israel out of our own self-interest."

Biden said he is a Zionist. "Israel is essential to security of Jews worldwide, and a state of Palestine -- each enjoying security, self-determination and mutual recognition," he said.

CNN's Laura Smith-Spark, Mike Pearson, Kareem Khadder, Michael Schwartz and Tim Lister contributed to this report.