The unprecedented challenge raised the temperature in a week-long crisis that has pitted a defiant Mr Erdogan against the Turkish judiciary and reignited anti-government sentiment which has simmered since the mass street-protests of mid-2013.
The resigning interior, economy and environment ministers each had a son detained last week as police went public with a long-running investigation into graft allegations involving state-run lender Halkbank.
Two of the sons remain in custody along with 22 others, including the head of the bank.
The first two ministers echoed the premier in deeming the probe a baseless plot against the government. However, Environment Minister Erdogan Bayraktar turned against the Turkish leader.
He said: "For the sake of the wellbeing of this nation and country, I believe the Prime Minister should resign."
By breaking ranks, Mr Bayraktar may have diluted any easing of pressure on Mr Erdogan afforded by the stepping-down of Interior Minister Muammer Guler and Economy Minister Zafer Caglayan.
While the cabinet shake-up's Christmas Day timing cushioned the blow to Turkey on dormant international markets, the country's stock index fell 3%.
Mr Erdogan did not immediately respond to Mr Bayraktar's remarks. However, in his first public appearance after the resignations, the Prime Minister, who during three terms in office has transformed Turkey by tackling its once-dominant secular military and orchestrating an economic boom, appeared unfazed.
Mr Erdogan told provincial leaders of his Islamist-rooted AK party he would not tolerate corruption.
However, having answered the arrests by purging police officers involved, he argued their work had been deeply tainted.
The Prime Minister said: "If a verdict is made by the opposition party on the second day of the investigation, what's the point of having judges?
"If a decision is made by the media, what's the point of having these long legal procedures?"
Alluding to reports which had riveted Turks with images of cash-filled shoeboxes allegedly seized at suspects' homes, he asked: "How do you know what that money is for?"
The 14-month probe was conducted largely in secret. At the weekend, the Erdogan government changed regulations for the police, requiring officers to report evidence, investigations, arrests and complaints to commanding officers and prosecutors.
The Hurriyet newspaper said as many as 550 police officers, including senior commanders, had been dismissed nationwide over the last week.
Erdogan critics see an authoritarian streak in his rule and the European Union, to which Turkey has long sought accession, urged Ankara on Tuesday to safeguard the separation of powers.
The latest scandal has laid bare rivalry between Mr Erdogan and Fethullah Gulen, a US-based Turkish cleric whose Hizmet movement claims at least one million followers, including senior police and judges, and runs schools and charities across Turkey and abroad.
While denying any role in the affair, Mr Gulen described Mr Erdogan as suffering "decayed thinking" after the premier portrayed himself as fending off a shadowy international plot.
In an apparent reference to Mr Gulen, Mr Erdogan said: "We would not let organisations acting under the guise of religion but being used as the tools of certain countries carry out an operation on our country."