Defense Minister Moshe Yaalon said Hamas has begun "paying a heavy price, both in terms of arrests and assets," suggesting the aim is to try to dismantle the Hamas infrastructure in the West Bank. It's not clear how far Israel will go, though, considering the risk of a conflagration in the West Bank after several years of relative calm.
Meanwhile, Israeli Prime Minister Benjamin Netanyahu has used the abductions to try to discredit Western-backed Palestinian President Mahmoud Abbas and the unity government Abbas formed with Hamas backing earlier this month.
Netanyahu claimed Abbas is ultimately responsible for the fate of the teens and alleged the Palestinian leader's new alliance with the Islamic militants created an atmosphere that encouraged the apparent kidnapping.
Abbas and Netanyahu spoke by phone Monday, a rare contact between the two. Netanyahu's office said the Israeli prime minister asked Abbas for help with the search.
"The Hamas kidnappers came from territory under Palestinian Authority control and returned to territory under Palestinian Authority control," Netanyahu told Abbas, referring to the areas where Palestinians have limited self-rule.
Abbas aides have rejected Netanyahu's contention, saying Israel is in overall control of the West Bank. The junction where the teens were last seen is under full Israeli security control and is commonly used by soldiers and settlers.
Abbas condemned both the apparent kidnapping and a "series of Israeli violations" in a statement Monday. He referred to the arrests and the killing of a 20-year-old Palestinian by Israeli army fire early Monday, during a confrontation between stone throwers and soldiers in a West Bank refugee camp.
Despite the pitched rhetoric, Palestinian security officials have worked with Israeli counterparts to try to locate the missing teens, Palestinian officials said.
Abbas has said such security coordination in the West Bank in place since Hamas seized the Gaza Strip from him in 2007 would continue even under a unity government. The joint efforts have routinely targeted Hamas activists.
The Israeli search for the missing students two 16-year-olds and a 19-year-old was concentrated in and around Hebron, the largest Palestinian city in the West Bank. Troops sealed the area, blocking access roads, and conducted house-to-house searches.
Arrests of Hamas activists began shortly after the teens disappeared. Several dozen more were rounded up overnight, including Abdel Aziz Dweik, the speaker of the parliament and a senior Hamas figure in the West Bank.
Hamas is considered a terror group by Israel and the West because of past attacks that have killed hundreds of Israeli soldiers and civilians.
Over the years, Israel has carried out periodic campaigns against the group, including arrest sweeps, but the current crackdown is the widest in the West Bank since 2006, when Israel retaliated for the capture of an Israeli soldier by Hamas-allied militants in Gaza. Separately, Israel has carried out several major offensives against Hamas in Gaza.
Israel has not provided evidence of Hamas involvement in the disappearance of the teens.
Israeli government spokesman Mark Regev said Monday that Israel waited for 48 hours before pointing the finger at Hamas. "The information is conclusive," he said. "The people behind the abduction are Hamas members."
Asked about Israel's claim, U.S. State Department spokeswoman Jen Psaki said that while Hamas has used similar tactics in the past, "I don't want to jump to a conclusion" at this time.
Hamas has praised the apparent abduction, but has stopped short of claiming responsibility. Other claims have emerged, including from a purported al-Qaida branch, but could not be authenticated.
Netanyahu said it could take time to track down the missing students, adding that "we are in the midst of a complex operation."
Officials have said they are working on the assumption the teens are alive, but four days without a sign of life is raising concerns.
One of the missing teens, Naftali Fraenkel, holds U.S. citizenship. Although he was born and raised in Israel, his family still has many relatives in the New York area.
On Monday, about 200 people gathered outside the Israeli consulate in New York, praying for the safe return of the three teens and the safety of the soldiers looking for them. Some carried signs with pictures of the teens and the phrase "Bring Back Our Boys."
"It's important for us, all Jews, to show support, to show that they're not forgotten, that we're together with them, we're worried about them," said Ethan Stein, 22, of Manhattan, a Brandeis University student who attended the rally.
The apparent abductions came at a time when Israeli-Palestinian tensions were already running high over the Palestinian unity government. Some senior Israeli officials called for a crackdown not just on Hamas, but also on Abbas' Palestinian Authority.
The incident has put Abbas in a bind.
He has repeatedly assured the U.S. and Europe that security coordination with Israel would continue under a unity government. But because such cooperation with Israel is widely unpopular among Palestinians, he cannot use it to counter Netanyahu's charges against him and the unity government. Highlighting it publicly could torpedo Palestinian reconciliation efforts.
Psaki, the State Department spokeswoman, signaled Monday that the apparent abductions have not changed Washington's view of the unity government.
"Based on what we know now, we do not believe that Hamas plays a role in the government," Psaki said.
Palestinian militants have repeatedly threatened to kidnap Israelis, hoping to use them as bargaining chips to win the release of prisoners held by Israel. No demands have been issued in connection with the disappearance of the three Israeli teens, however.
Currently, dozens of Palestinians held by Israel are on a hunger strike to try to force Israel to end the practice of "administrative detentions" without charges or trial.
Laub reported from Jericho, West Bank. Associated Press writer Nasser Shiyoukhi in Hebron, West Bank, Matthew Lee in Washington and Deepti Hajela in New York contributed to this report.