Thousands of Israelis marched in Tel Aviv at the weekend in the biggest demonstration for years to protest against a series of attacks on civil and human rights organisations and a rise in anti-Arab sentiment.

Under the banner of the "Democratic Camp", a coalition of organisations and prominent individuals, the marchers heard speakers lambast the Israeli government, singling out the rightwing foreign minister, Avigdor Lieberman, who is seen as threatening Israel's democracy.

But there was also strong criticism of the Labour party for being a partner in Binyamin Netanyahu's coalition government. Labour had allowed "the existence of the most racist coalition in the history of Israel", Nitzan Horowitz, a member of the Knesset for the leftwing Meretz party, told the crowd. "No member of the Labour party can claim to have clean hands. You are members of the most extreme government … For what have you betrayed your principles? For a few ministers' chairs?"

The organisers of the march and rally hoped it would signal the beginning of the revival of Israel's left and a fightback against the dominance of the right. Around 20,000 people attended the rally according to the organisers; the police said there were 10,000 present.

The galvanising issue was the recent approval by the Knesset of a bill to set up a parliamentary investigation into the funding of civil and human rights groups. It has been seen by opponents across the political spectrum as a fundamental attack on democracy and reminiscent of a McCarthyite witch-hunt.

Following the vote, the opposition leader, Tzipi Livni, said an evil wind was blowing across Israel. Some in the crowd on Saturday evening held placards saying "Investigate me too".

Speakers at the rally cited other recent moves including a call by rabbis to ban Jews from selling or renting property to Arabs, a parliamentary vote in favour of a "loyalty oath" to be taken by new Israeli citizens, and the jailing of the activist Jonathan Pollack after taking part in a bicycle protest.

Addressing the rally, Meir Sheetrit of the centre-right Kadima party said legislation to investigate rights groups would be "taking a brick out of the wall of democracy".

Avraham Burg, a former Knesset speaker and a driving force behind the embryonic Democratic Camp, told the Guardian the situation was "an emergency".

"Israel is not a democracy any more. Technically it is, but the foundations of democracy – liberty, equality – are under threat. The rabbinical fatwas and political harassment are red lights. If we don't stand up now, tomorrow it will be too late."

For a long time, he said, the left had been passive. The Democratic Camp "is not yet big, but it's a beginning. This is the launching pad for the future political generation of Israel".

Protesters held placards reading "Jews and Arabs will not be enemies" and "We will fight the regime of darkness", and both Israeli and Palestinian flags were waved. One participant said "it must be the end of the world" for her to join a demonstration on a Saturday evening.