The bodies of three missing Israeli teenagers who disappeared almost three weeks ago have been found buried in a shallow grave under rocks in a valley close to the southern West Bank city of Hebron.

Following the discovery of the bodies the Israeli prime minister, Binyamin Netanyahu, blamed Hamas for the murders, warning the militant group will pay a heavy price for the deaths. "Hamas is responsible, and Hamas will pay ... [They] were kidnapped and murdered in cold blood by wild beasts," Netanyahu said in a statement.

Israeli soldiers and civilian volunteers found two bodies at 5pm on Monday in a shallow grave covered with boulders, later uncovering a third body. Although there was no immediate confirmation of their identity, both the location, close to where they went missing, and the number of bodies pointed inescapably to it being the remains of the three teenagers.

"The bodies are currently going through forensic identification. The families of the abducted teens have been notified," a senior spokesman for the army said on Monday evening.

An Israeli woman with a photo of the teenagers at a rally in Tel Aviv on Sunday. Photograph: Baz Ratner/Reuters

Eyal Yifrach, 19, Gilad Shaar, 16, and Naftali Frankel, 16, went missing while hitchhiking back from their religious schools in settlements on the West Bank on 10 June.

According to reports in the Israeli media on Monday it appeared the three were killed shortly after being abducted near the Gush Etzion junction in the southern West Bank. The same reports suggested they were shot in the car they got into, which was later discovered abandoned and burned out.

"There can be no forgiveness for the killers of children and those who sent them. Now is the time to act," Israel's economy minister, Naftali Bennett, said in a statement.

Separately, Palestinian president Mahmoud Abbas called an emergency meeting to discuss the killings.

A senior Hamas spokesman, however, denied the group's involvement. "Only the Israeli version of the events has been published," said Sami Abu Zuhri. "Israel is attempting to make way for aggression against us, against the Hamas … No Palestinian group, Hamas or any other group, has taken responsibility for the action, and thus the Israeli version can't be trusted."

The hunt for the three missing youths has seen several hundred Palestinians rounded up in a massive operation – often without charge or connection to the kidnapping – and five Palestinians, including a number of minors, killed.

The official announcement by the Israeli military and the Shin Bet security agency that the bodies had been found followed hours of swirling rumours in Israel where the hunt for the missing youths has galvanised Israeli society, prompting round-the-clock coverage and large rallies – the most recent in Tel Aviv on Sunday – calling for their release.

An army spokesman said the bodies had been buried in a field near the village of Halhul just north of one of the entrances to Hebron.

Binyamin Proper, who was among the civilian volunteers who found the bodies, told Channel 2 TV that a member of the search party "saw something suspicious on the ground, plants that looked out of place, moved them and moved some rocks and then found the bodies. We realised it was them and we called the army."

Outside the home of Eyal Yifrach, one of the missing teenagers, the street was packed with Orthodox Jews, standing behind a police barricade and listening to the news on the radio.

An elderly woman who declined to give her name to the Guardian wept as she spoke of the deaths of the teenagers. "We need to do to them as they have done to us," she said. "We see lots of Arabs in the malls, in the shops. We don't do what they do. They used to eat with us and now they kill us."

Yvette, 36, a neighbour, said: "When the Arabs are doing the killing the world stays silent, it is always Israel [who is criticised]."

On the streets surrounding the neighbourhood, families stood on balconies. Everyone was listening to a radio. TV cameras were directly outside the Yifrach house, which was closed off.

The case prompted a massive manhunt by soldiers, police and members of Israel's domestic intelligence agency, Shin Bet. As the search went on concerns mounted for the teenagers' safety, amid pointed and grim reminders in the Israeli media that West Bank kidnapping victims historically have often been killed shortly after their abduction.

The abduction of the three youths has also become a heated political issue both on the domestic and international political front, with Palestinian leaders accusing the Israeli government of using it as an excuse to smash the new Palestinian unity government backed by Hamas.

However, even within Palestinian circles close to Abbas, concerns had been growing over the potential fallout that would follow the revelation that the teenagers had been kidnapped or killed by militants associated with – or members of – Hamas, with one official telling the Guardian the unity government would be dead in the water.

US President Barack Obama condemned what he called the "senseless" murder of the teenagers and warned against actions that could further "destabilise" the situation. "The United States condemns in the strongest possible terms this senseless act of terror against innocent youth," Obama said in a written statement.

In a statement issue by his office British prime minister David Cameron said: "I am deeply saddened by the news that the bodies of the three Israeli boys ... have been found ... This was an appalling and inexcusable act of terror perpetrated against young teenagers. Britain will stand with Israel as it seeks to bring to justice those responsible."

In Nof Ayalon, where Naftali Frankel lived, groups of friends, family and neighbours of the 16-year-old walked arm and arm through the quiet streets.

The contrast as the residents gathered at the local synagogue was palpable to El Ad a short drive away. Both male and female sides of the synagogue were packed but largely quiet, unlike the scenes at the Yifrach neighbourhood.

A 16-year-old fellow student of Frankel, sitting outside on a bench smoking, said that although many had criticised the three students for hitchhiking, he knew many pupils at the yeshiva they attended and the killings would not stop him or them from doing it.

"I am mad, but I am not going to get too excited about it," he said. Asked what he wanted the aftermath of the killings to be he said: "Peace."