Activists behind spiralling protests in Israel plan to build on one of the biggest marches ever seen in the country by piling on "more pressure, more people, more tents and more protests" culminating in a million-strong march in 50 cities next month.

An estimated 300,000 people took to the streets on Saturday to press their demands for social justice and lower living costs in the largest demonstrations over social issues ever seen in the country. Despite scepticism that turnout could surpass previous events, almost twice as many people joined marches in Tel Aviv, Jerusalem and other towns and cities.

Binyamin Netanyahu, Israel's prime minister, was forced to respond to the spiralling protests with the establishment of a committee to "listen to the distress" and recommend action.

The protests, which began with a handful of tents erected in Tel Aviv, have unleashed a national fury at the government's failure to respond to the needs and complaints of middle-income Israelis. Tent cities have mushroomed in more than 40 locations across the country as well as daily demonstrations and roadblocks over the cost of housing, childcare, fuel, food and electricity.

Despite Israel's relatively healthy economic growth and low unemployment, wage disparities are big, wealth and corporate power are highly concentrated, food prices have increased almost 13% since 2005 and many people spend 50% of their incomes on rent or mortgages.

Up to 250,000 people marched through Tel Aviv to Israel's military headquarters on Saturday, causing major traffic diversions until the early hours. One sign, in Hebrew and Arabic, read "Egypt is here".

In Jerusalem, up to 30,000 people marched to Netanyahu's residence, chanting the rallying cry of the past three weeks: "The people demand social justice." Smaller protests were also held in Kiryat Shmona, Modi'in, Hod HaSharon, Ashkelon, Eilat and Dimona, according to media reports.

Stav Shaffir, 26, one of the original tent protesters in Tel Aviv, told the Guardian that "more pressure, more people, more tents and more protests" would follow. "Right now we're coming together to think about our next steps. There will be more protests – definitely more protests."

A loose alliance of activists behind the protests called for a million-strong march on 3 September.

The committee set up by Netanyahu was ordered to report within a month. "It is impossible to ignore the voices coming from the public," the prime minister said in a lengthy statement. Israel's economy was strong, but "we know that we must make the internal corrections ... social corrections, with sensitivity".

He added: "We will listen to everyone. We will speak with everyone." However, Netanyahu has so far refused to meet a delegation from the tent protesters.

"This is definitely not enough," said Shaffir. "We have been on the street for almost a month, and there has been no contact at all from Netanyahu. The public thinks the government is out of touch with the people, and people are angry and want to see change."Shimon Peres, Israel's president, said the protests were a "testament to the nation's maturity". In contrast, the extreme right foreign minister, Avigdor Lieberman, said that cafes in Tel Aviv were "packed to capacity" adding that there was no reason "to be depressed".

The social protests have become the most pressing issue for the Israeli government, with the potential, according to some commentators, to topple Netanyahu's coalition. Opinion polls have put public support for the protests at around 90%. Protest leaders have insisted that bringing the government down is not their aim.

The organisers have striven to keep the movement as inclusive as possible, incorporating left and right, secular and religious, Jews and Arabs.

They have avoided publicly making connections between the amount spent on settlements and the military for fear of being branded anti-occupation activists.

"It is certainly one of the largest street protests we have experienced in Israel," said Tamar Hermann, of the Israel Democracy Institute. "But what really makes it different is its heterogeneous nature. Normally protest is homogeneous. Diversity is as important as size."

She said Israel's economic health was "one of the reasons people feel able to protest. When you are at rock bottom you invest everything in survival. People here are not devastated but discontented."

Avraham Burg, a former speaker of the Israeli parliament, said the protests would define Israeli society as "a collective based either on social solidarity or national territorialism".

Indications that the former was outgunning the latter were "why all the settlers are so upset", he added.

Some observers believe Netanyahu will try to ride out the protests until September, when the Palestinian bid for statehood at the United Nations is likely to dominate the political agenda. The Palestinians, they say, are a familiar foe that Netanyahu feels he can outmanoeuvre whereas the Israeli social justice protesters are an unknown force.

Analogies drawn between the Arab spring and the Israeli summer were not completely misplaced, according to Hermann. "Israelis generally want to disassociate themselves from the Middle East, culturally, politically and economically. But obviously they have watched Tahrir Square as well as events in Spain and Athens.

"Protest is a phenomenon which often spills over national borders. This fits into a new wave of street protests that we are now seeing all over the world, including the Middle East."

Palestinian demands

As Israelis take to the streets to demand social justice, Palestinians are also gearing up to protest next month over their demands for recognition of a Palestinian state by the United Nations.

President Mahmoud Abbas has urged "popular resistance" as well as diplomatic moves. "In this coming period, we want mass action, organised and co-ordinated in every place," he said last month. "This is a chance to raise our voices in front of the world and say we want our rights."

Marwan Barghouti, an iconic figure for Palestinians who is serving five life sentences in an Israeli jail, also called for mass action. "I call on our people in the homeland and in the diaspora to go out in a peaceful, million-man march during the week of voting in the United Nations in September," he said.

Palestinian leaders, backed by the Arab League, intend to ask the UN general assembly to back a Palestinian state when it meets in September. However, full recognition requires the backing of the UN security council, which the US has vowed to veto.

The Israeli protests are being given scant attention in the Palestinian media. But, said Mustafa Barghouti, a member of the Palestinian parliament, "we feel sympathetic because they are also demanding social rights. At the same time we hope that they will see that one of the reasons for this crisis is the Israeli occupation policy and military spending. "We hope that this social movement becomes a political movement which demands peace and end to occupation." Harriet Sherwood