Fears are growing for the safety of three Israeli teenagers believed to have been kidnapped in the southern West Bank by Palestinian militants, after the Israeli army said that it could not confirm if they are alive or dead.

The three boys, one of them a US citizen, lived in nearby settlements. They disappeared on Thursday night from a hitch-hiking spot near Kfar Etzion in the Hebron hills. They were named late on Saturday as Eyal Yifrah, 19, Gil-Ad Sha'ar, 16, and Naftali Frenkel, 16.

Israeli prime minister Binyamin Netanyahu said there was "no doubt the three had been kidnapped by a terrorist organisation", although he did not name the group allegedly responsible.

"Our children were kidnapped by a terror group, no doubt about that," he said. He added that there was an "intensive operation" under way to prevent them from being taken to the Gaza Strip or elsewhere. Netanyahu said he held the Palestinian president, Mahmoud Abbas, and the Palestinian Authority responsible.

The three were returning to their homes for the sabbath from two religious schools nearby when they disappeared. Since then members of the Israeli military, including paratroopers and police and intelligence officers, have swamped the area in the search for the missing youths.

A military source told Reuters it had preliminary information about the captors' identities. This was echoed by remarks on Israeli radio that progress had been made in identifying the kidnappers.

There was a welter of speculation in the Israeli media, including suggestions that the kidnappers might be planning to take the teenagers to Gaza or across the border to Jordan, and unconfirmed reports of arrests. Israeli television broke into football World Cup coverage with updates on Friday night.

Netanyahu convened the security cabinet to take charge of the search as commentators said that, historically, victims of abductions by Palestinian groups on the West Bank had been killed shortly after their capture. The bleak prognosis is based on the fact that, unlike in Gaza, Israeli intelligence penetration of the West Bank is known to be so great that kidnappers would find it hard to hide their captives for long.

The defence minister, Moshe Ya'alon, told reporters on Saturday that the search would continue based on the belief that the boys were alive. "As long as we don't know differently," said Ya'alon, "our working assumption is that they are alive."

Adnan Demeiri, a spokesman for the Palestinian security services, said the Palestinian Authority was not responsible and pointed out that the boys disappeared in an area under full Israeli security control.

A burned-out stolen car with Israeli number plates was found which, it has been suggested, may be linked to the missing youths. Palestinians in and around the city of Hebron, which has been the focus of the search, said those detained for questioning by Israeli security forces were largely involved in car businesses, such as repair garages, indicating that the investigation was focusing on tracking down potential means of transport. Witnesses described seeing troops taking footage from privately owned security cameras.

The disappearance comes amid sharply heightened tension between Palestinians and Israelis after the collapse of peace talks in April and the subsequent formation of a Palestinian unity government backed by the Islamist group Hamas, which is considered a terrorist group by Israel and the west.

On Saturday, militants in the Gaza Strip fired a rocket at southern Israel, the military said, adding that nobody was hurt in the attack. Soon after, Israel retaliated with an air strike on what it described as "a terror activity site and a weapon storage facility" in Gaza. There were no reports of injuries.

The US secretary of state, John Kerry, who had been brokering peace talks between Israel and the Palestinians before their collapse earlier this year, spoke to Netanyahu and Abbas about the missing teenagers on Friday night.

Netanyahu's office said he told Kerry: "This is the result of a murderous terror organisation entering the government."

Meanwhile it was also reported that a seven-year-old Palestinian girl injured during an Israeli air strike on Wednesday had died of her wounds.

Last year, a Palestinian man brought an Israeli soldier into a West Bank village and killed him in the hope of trading the body for his jailed brother.

In 2001, a Palestinian woman used the internet to lure an Israeli teenage boy to the West Bank where he was killed by waiting Palestinian gunmen.

The woman, Amna Muna, was released in 2011 along with more than 1,000 other Palestinian prisoners in exchange for the Israeli soldier Gilad Shalit, who had been held captive in Gaza by Hamas-allied militants for more than five years.