Hundreds of people attended the funeral of 20-year-old Moshe Malko at the Mount Herzl military cemetery in Jerusalem, one of a series of burials for the 13 soldiers killed in Gaza on Sunday.

As his coffin, draped in an Israeli flag was lowered from a military jeep, wails and sobs erupted from members of the Ethiopian Jewish community, of which Malko was a member. The coffin was accompanied to a grave by a phalanx of uniformed young soldiers, many in tears. Community elders, dressed in white shawls and turbans, stood close by.

Tomer Siyonov, 22, a friend of the dead soldier, who finished his own compulsory army service two months ago, drew deeply on a cigarette as the eulogies were delivered. "Hamas killed my friend; we need to kill them – not just the Hamas militants but all the people in Gaza," he said.

"What else should we do? Lose more friends? We don't have a choice – if we don't fight to the end, they will kill us."

A young woman, one of three crying throughout the funeral, had been to school with Malko. Asked about what should now happen in Gaza, she was guarded. "It's complicated," was all she said before turning to comfort her friends.

Elsewhere in Jerusalem, support for the military offensive appeared to be hardening despite the rising casualties on both sides.

"All of our people are united," said Gal Tuttnauer, 25, eating shawarma in the city centre. "Of course I'm against a ceasefire, we need to continue. Hamas needs to be wiped out, and that will take time."

The international media, he said, was duped into showing images of dead children in Gaza without explaining the context to the conflict.

"Why isn't the foreign media talking about what's happening in Syria? Israel is seen as the black sheep. No one cares about Israel, because Hamas and the Palestinians are the underdogs, and everyone likes an underdog. They have rockets and we have a big army, so we're the always the bad guys."

Asher Dobol, 57, whose son is currently fighting in Gaza, said: "Of course I'm worried about him, but – this time – everyone thinks the government must not stop until they've destroyed all the tunnels. It was right to go in [on the ground]. We must destroy Hamas and take over Gaza."

In contrast to previous conflicts, he added, "this time the world is supporting Israel. The world understands we cannot live under rocket fire."

Both men said they regretted Palestinian civilian casualties, but blamed Hamas rather than the Israeli army. "A lot of people were killed in Shujai'iya because Hamas uses them as human shields," said Tuttnauer, adding: "Palestinians don't care about human life, whereas we appreciate life. We want to live, they want to die."

Support for the military operation is strong, but not universal, among Israelis. Demonstrations and rallies calling for peace have attracted small numbers, but one in Tel Aviv on Saturday evening mustered about 1,000 people. Like previous peace protests, it was attacked by rightwing activists, who threw eggs and plastic bottles.

In Haifa, a mixed city, an anti-war protest on the same day was confronted with rightwingers, chanting: "Death to Arabs". The city's Israeli-Arab deputy mayor and his son were beaten up.

Following Sunday's bloodshed in Shujai'iya, Israeli-Arabs called for a day of mourning and a general strike, which was largely observed in Arab towns in the north of the country. Avigdor Lieberman, Israel's hawkish foreign minister, called on Israeli Jews to boycott Arab businesses in response.

The peace camp, once a vocal part of Israeli political discourse, has struggled in recent years as the centre of political gravity has shifted to the right and successive attempts to broker a peace deal between Israel and the Palestinians have failed.

Attempts by the right to pass laws which limit the capacity of pro-peace organisations and campaigners to operate effectively have also sapped the confidence of and support for the Israeli left.

Haggai Matar, 30, an Israeli journalist and political activist, said the actions and statements of many Israeli politicians fuelled the far right.

"We have seen politicians passing bills against human rights NGOs … and very high-ranking politicians saying that the NGOs and leftists are a cancer and are traitors and trying to destroy our society – these are not words of regular democratic or political conflict," he said, adding that young people in Israel were now often more rightwing than their parents.

"Our parents would remember having gone to Palestinian cities for shopping or seen more Palestinian workers coming into Israel. It was never an equal relationship but it was a chance to meet, and that you haven't had for 20 years or more," he said.

Rhoel Chaguel and her daughter, Ron, epitomise that generational change in attitudes among many Israelis towards their Palestinian neighbours.

Rhoel, a mother of three whose family were Arabic-speaking Jews from Morocco, had spent time in hospital recently with her son, Simon, and met families from Gaza who were being treated there. Rhoel conversed with the mothers, and often brought them clothes and food. "They are afraid of Hamas," she said.

Ron, 17, and just six months away from beginning her national service, which she plans to spend working in a hospital rather than serve in the military, disagreed. "When they are healthy they will go back to Gaza, these boys," she said. "They will grow up and become terrorists."