The Israeli prime minister, Binyamin Netanyahu, is facing a bout of political turbulence after leading Israel through a seven-week war against Hamas in Gaza – a conflict that has caused a rift in his cabinet and drawn deep public scepticism.

Some observers are predicting an election next year after this week's ceasefire deal gave no clearly definable gains to either side in the conflict. However, at present there is no strong and credible challenger to Netanyahu, who is serving his third term as prime minister at the head of a coalition government.

Netanyahu, defence minister Moshe Ya'alon and military chief of staff Benny Gantz gave a press conference, broadcast live on Israel's main television channels, on Wednesday evening at which they presented the conclusion of the war as a military and political triumph for Israel.

Israel had secured a "great military accomplishment and a great diplomatic achievement" in the conflict, and Hamas had been dealt a "heavy blow", Netanyahu said. "From the start, we set a clear goal and that was to inflict serious damage on Hamas and the other terrorist groups and by doing so to bring extended quiet to all Israel's citizens," the prime minister said.

"Hamas was seriously beaten. We destroyed the tunnel systems which it built for years. In addition, Hamas is diplomatically isolated. Will we reach our goal of long-term quiet? I think that it is still too early to tell, but I can say that the severe damage caused to Hamas and to the terror organisations, and our ability to prevent them from rearming themselves by controlling the borders, those will increase the chances for this goal's implementation."

The Israeli public, however, was apparently not convinced. A poll published in Haaretz newspaper found that 54% of those surveyed believed there was no clear winner in the 50-day war.

Four cabinet ministers – including foreign minister Avigdor Lieberman and economy minister Naftali Bennett, both hardliners to the right of Netanyahu – opposed reaching a deal with Hamas to end the war, although no cabinet vote was taken on the agreement. During the conflict, Lieberman and Bennett advocated a harsher military strategy aimed at toppling Hamas and taking over the Gaza Strip.

Media commentators were scathing about Netanyahu's claim of beating Hamas. Ben Caspit, a hawkish columnist for the newspaper Ma'ariv, wrote: "The paradox is that most of what Netanyahu, Ya'alon and Gantz said yesterday was correct. Yes, Hamas did take a very bad blow. Yes, the IDF did have many achievements. Yes, Hamas had no achievement in this war. But yes, we too, in the meantime, have achieved nothing. It could have been expected that the State of Israel, with the IDF, the GSS [security service], the Mossad, the Air Force and the best intelligence in the world, could have defeated Hamas, or at least dictated the pace of events and the timetable. In reality, Hamas dictated them."

A former director of Israel's Shin Bet security service, Yuval Diskin, said the war's results "were disappointing and were accompanied by what some have described as a sense of sourness". Writing in Yedioth Ahronoth, he added: "The ceasefire that was achieved with Hamas has left the Israeli public frustrated."

That frustration appeared to be reflected in two polls this week. A survey by Channel Two found that 59% of those questioned did not agree that Israel had won against Hamas, while the poll for Haaretz found that 54% of people thought there was no winner, around a quarter said Israel had won, and 16% thought Hamas had won.

But in an indication of the lack of political alternatives to Netanyahu, 42% of respondents in the Haaretz poll put him at the top of a list of politicians most suited to be prime minister. Next were the Labour leader, Isaac Herzog, on 12%, and Lieberman and Bennett, both on 11%. One in five people said they did not know who was best suited for the job.

Residents of villages close to the Israel-Gaza border, who bore the brunt of rocket and mortar fire, have expressed anxiety about their security and the viability of their communities if attacks resume in the future. Despite the indefinite ceasefire, many families have yet to return to their homes after relocating to relatively safer areas further from Gaza.

• Anshel Pfeffer, Comment is free