Turkish opposition parties called on the prime minister to resign on Tuesday as a result of an explosive corruption scandal in which he was allegedly caught on tape ordering his son to get rid of millions of dollars in incriminating cash.

Recep Tayyip Erdogan responded in characteristically robust form, dismissing the allegations against him as a plot to bring down his government – the latest in a wave of accusations fuelling widespread popular protest against his 11-year rule.

Recordings of phone-tapped conversations leaked on the internet appear to capture Erdogan instructing his 33-year-old son, Bilal, to dispose of large amounts of hidden funds from their private home in the midst of a corruption investigation.

Erdogan has rejected the allegations as "complete lies", insisting the recordings were fabricated to discredit his government. "Yesterday they published a play that they have assembled and dubbed themselves," he told a meeting of his ruling Justice and Development party (AKP). "What has been done is a vile attack against the Republic of Turkey and her prime minister. If we bow to this, we will be doing injustice to all coming prime ministers and ministers."

In the recording, a man alleged to be Erdogan tells his son to dispose of tens of millions as investigators are searching the homes of relatives of three cabinet ministers "for a big corruption operation".

"OK, so what I am saying is, get all that stuff in your house out. OK?" he says.

A voice alleged to be that of his son, Billal replies: "Dad, could that be? There is your money in the safe." The older man's voice responds: "That's what I mean."

Later, the person alleged to be the prime minister asks: "Did you make most of it vanish?" He is answered: "We haven't been able to do all of it yet. There are about 30m euros left. We haven't been able to get that out yet."

Erdogan described the recordings as "blackmail, being spread via Twitter".

But he admitted his phone had been tapped in what he called "Turkey's biggest eavesdropping scandal of all times".

Pro-government newspapers have claimed that thousands of government officials, academics, business people and journalists have been listened to illegally. It has been impossible to verify the authenticity of the recordings, which first appeared on YouTube but quickly spread across social media sites. Even so, they are likely to inflict a painful political blow.

The alleged conversation is said to have taken place on 17 December last year – a day on which police conducted a series of surprise raids that resulted in the arrest of the sons of three government ministers and several high-profile businessmen.

Since December, Erdogan has removed or fired the key people involved in these investigations, reappointed thousands of police officials and prosecutors, and rushed through laws tightening government control over the judiciary and prosecution services.

He has repeatedly blamed the US-based Islamic cleric Fethullah Gülen – a former ally – for orchestrating what he says is a campaign aimed at toppling the government.

Erogan has held emergency meetings with the head of the Turkish secret intelligence agency, Hakan Fidan, since the recordings emerged, Turkish media has reported. The prime minister's office has issued a statement threatening legal action against anyone who circulated them.

The main opposition Republican People's party (CHP) has demanded that Erdogan resign. Speaking at a party meeting on Tuesday, the CHP leader, Kemal Kilicdaroglu, said there was little doubt about the authenticity of the recordings and that the government had lost its legitimacy.

"Take your helicopter and flee, go abroad, or resign from the prime ministry. Someone who robs the country cannot sit in the seat of a prime minister," he said.

Devlet Bahceli, head of the right-wing National Movement party (MHP), used equally damning words in local election rally speech on Tuesday: "This is a very critical moment for Turkey. Hunger, injustice, immorality, corruption and bribery are amongst Turkey's main problems. This is the image we have of eleven years of [the AKP's rule].

said: "There are signs that the prime minister is at the head of corruption in Turkey. The prime minister speaks of a plot. If it really is a lie and a plot, it should be proven to the people. But if any of this is true, he cannot remain prime minister for even one second longer. The prosecution has to act."

Others in the opposition, however, cautioned against action that would plunge Turkey further into chaos. The co-chair of the pro-Kurdish Peace and Democracy party, Selahattin Demirtas, said that all responsible parties should be brought to justice.

"The only things the prime minister should do is to let justice take its course. You might not save yourself, but you might save this country, with more transparency and more democracy."