Three Turkish ministers resigned this morning, a week after their sons were detained in a sweeping corruption investigation that pits Tayyip Erdogan's government against the judiciary.

One of those stepping down, Environment and Urbanisation Minister Erdogan Bayraktar, urged the prime minister to follow suit.

It was an unprecedented challenge to the Turkish leader, who has cast the scandal as a foreign-orchestrated plot and purged police in response.

"For the sake of the wellbeing of this nation and country, I believe the prime minister should resign," Mr Bayraktar, whose son was briefly detained in the case that erupted on 17 December, told NTV news.

The other cabinet members who resigned, Minister Muammer Guler and Economy Minister Zafer Caglayan, have a son each among the 24 people still in police custody on graft charges.

They denied any wrongdoing by their sons or the government.   

"I have resigned from my post of economy minister to help the truth to come out and to foil this ugly plot, which has impacted my child and my close work colleagues among others," Mr Caglayan said in a statement.

In a separate statement, Mr Guler called the 17 December arrests "a dirty set-up against our government, party and country".