Celebratory bursts of gunfire, cheering and chanting could be heard within minutes of the ceasefire between Israel and Hamas coming into effect on Wednesday as gunmen emerged on the streets of Gaza City to claim victory.

Some people let off fireworks from rooftops. Others drove through the city with horns blaring. But in Israel, relief at the war's end was imbued with caution, scepticism and opposition to striking a deal with Hamas. Many were waiting to see if the deal would hold before celebrating.

Along Gaza City's waterfront, a loudspeaker on a mosque repeated over and over: Allahu Akbar. "Israel begged for a ceasefire because it could not stop our rockets," said Adel Mansour. "They bombed us, they killed our women and children, but they could not stop the resistance. So they had to surrender and agree to stop the assassinations. They learned we cannot be defeated by their bombs."

Support for Hamas has strengthened inside Gaza in recent days because it has been seen to stand up to Israel. There is little debate about the cost in lives. "Our martyrs are the price we must pay," said Mansour. "But it is the Israelis who have their blood on their hands."

Right up to the 9pm local time deadline for the ceasefire to kick in, Gaza City continued to be rocked by massive blasts. At least one person was killed in the final minutes of fighting.

Hamas "resistance" – through the barrage of rockets into Israel – is seen as having deterred a ground invasion and forced the Israelis into an agreement to stop targeted assassinations.

The ceasefire brought relief and a halt to the rising death toll. More than 140 people have been killed in Gaza in the past eight days, while five Israelis lost their lives.

In Israel, there was significant opposition to the deal. A snap poll by Israel's Channel 2 found that 70% did not support signing a ceasefire with Hamas, with just 24% in favour.

Some residents in southern cities took to the streets on Wednesday to protest against the deal, Israeli television reported. All schools and businesses within 25 miles of Gaza were to remain closed on Thursday.

David Magriso, a lawyer who earlier rushed to the scene of Wednesday's Tel Aviv bus bombing from his nearby offices when he heard the blast, said: "I want to be optimistic, but I can't rule out being pessimistic. We hope that we will have quiet. I have no doubt that it will hold from our side, but terror organisations do not have the same discipline."

That view was echoed by other Israelis who have spent the past week under a barrage of rocket fire from Gaza. Ya'ara Menachim, a teacher in Sderot, the town closest to the Gaza border, said: "This is a pause, not a peace. We don't believe in ceasefires any more."

Zmira Ben Yosef, the headmaster of a school that has been closed for the past eight days, said: "I just want this to be over. For the past two hours there has been silence, and I hope it will go on. But I don't trust Hamas."

Earlier, several of those milling around the site of the bus bombing had insisted that Israel should fight on, with troops and tanks on the ground in Gaza. "We need to finish this war for once and for all," said an onlooker.

Paramedic Israel Kornik, clad in bright blue surgical gloves and a reflective jacket, said he had helped a bloodied woman passenger off the wrecked bus.

"She cried like a baby," he said. "As I took her to the ambulance, she said 'tell [prime minister] Binyamin Netanyahu to be strong. Don't stop, finish the job [in Gaza], go forward'."

Following the blast, in which 15 Israelis were injured, Danny Danon, the deputy speaker of Israel's parliament, urged an immediate ground invasion of Gaza. "It is time to declare war. The time for restraint is over," he tweeted.

The blast revived traumatic memories of past bombings of buses, cafes and other public places. It was the first such attack in Tel Aviv since 2006.

Tamara Kessel, 54, who was standing next to the bus at the time, lost her unborn child in a bus bombing in the city in 1996. "I heard the blast, and fell to the ground," she said, still shaking with shock more than an hour later. "This was the last thing I was expecting. You cannot live like this. All these traumas – it just goes on."

Chaim Shafir, who lives nearby, said he had been expecting a violent attack in the city.

"Paradoxically, maybe this will do some good. People only stop fighting when both sides realise there is no point. Maybe some sense will start to emerge."

During the eight-day war, the Israeli military targeted more than 1,500 sites in Gaza with airstrikes and shelling. It said more than 1,000 rockets had been fired at Israel.