Michael Gove made a thinly veiled swipe at senior Tories caught in a fake company sting, saying their first duty is “towards their constituents”.
The levelling up secretary said it was important that MPs do everything they can to “put public service first”.
He made the comments after Matt Hancock and Kwasi Kwarteng told a fake overseas company their daily rate for consultancy would be £10,000.
Gove told Sky News’ Sophy Ridge On Sunday programme that the MPs caught up in the sting had been operating “within the rules”.
He added: “But inevitably all of us will reflect on this and think the first duty of a member of parliament is towards their constituents.
“And ultimately, the really important thing is, is an MP delivering for their constituents, is a member of parliament doing everything they can to put public service first?”
The sting operation was set up by anti-Brexit campaign group Led By Donkeys in which they pretended to be a South Korean firm looking for MPs advisers.
Former cabinet ministers Hancock and Kwarteng both set out six-figure sums for what they would expect to be paid to advise the non-existent firm.
There is no accusation of wrongdoing because MPs are allowed to seek employment outside of parliament.
However, second jobs have come under the spotlight in recent years, following former Tory cabinet minister Owen Paterson’s suspension from the Commons for breaching lobbying rules in 2021.
Critics say being an MP should be a full-time job and MPs should not be using their taxpayer funded offices to make such negotiations.
Asked if he had a daily rate during a fake online interview, Hancock said: “I do, yes. It is 10,000 sterling.”
The former health secretary, who was stripped of the party whip by prime minister Rishi Sunak after he went on I’m A Celebrity… Get Me Out Of Here!, also said he had an hourly rate of “around £1,500”.
A spokesman for Hancock said the West Suffolk MP had “acted entirely properly and within the rules”.
Former Tory chancellor Kwarteng, when asked the same question, said: “I would say as an MP, obviously I don’t need to earn a king’s ransom.
“But I wouldn’t do anything less than for about 10,000 dollars a month.”
Kwarteng, whose mini-budget in September sent the value of the pound tumbling and mortgage rates soaring, went on to clarify that he would prefer the rate to be in pound sterling.
Led By Donkeys created a sham company, called Hanseong Consulting, by setting up a website and paying for a “fake virtual office” in the South Korean capital Seoul.
They approached 20 MPs from different parties asking if they would join the firm’s international advisory board.
Led By Donkeys said 16 of the MPs approached were Tory, two Labour, one a Liberal Democrat and the other an independent.
Out of those contacted, five are said to have progressed to an online interview stage, including Hancock and four Tories: Kwarteng, former education secretary Sir Gavin Williamson, former minister Stephen Hammond and Sir Graham Brady, chairman of the powerful 1922 Committee.
Brady, according to the video, said he was “thinking something like £60,000 as an annual rate” for assisting the firm.
Brady said he made clear to those behind the hoax that any work would have to fall “within the terms of the code of conduct”.
No details of what Hammond said have been released and Led By Donkeys said Williamson turned down the opportunity to take discussions any further.
A spokesperson for Hancock said: “The accusation appears to be that Matt acted entirely properly and within the rules, which had just been unanimously adopted by Parliament.
“It’s completely untrue to suggest any wrongdoing and therefore absurd to bring Mr Hancock into this story through the illegal publication of a private conversation. All the video shows is Matt acting completely properly.”
Brady said: “Having decided to leave the Commons at the next election, I have received a number of approaches regarding future opportunities.
“I did have an exploratory discussion with someone purporting to be recruiting an international advisory board for a South Korean investment house.
“I made it clear that any arrangement would have to be completely transparent and that whilst a member of parliament, I would only act within the terms of the code of conduct.
“I also made it clear that whilst I could be flexible in attending international meetings in person, this would be subject to some important votes or commitments in Westminster.”
Shadow culture secretary Lucy Powell said she was “pretty appalled and sickened” by the revelations, adding “there is a problem with the rules”.
She added: “Being an MP is absolutely a full-time job, it’s not just a full-time job, it’s a whole lifetime commitment and our constituents need us to be fully focused on that, not working out whether we’ve got other interests and whether we are pursuing other commercial ends in our doing our job.”
She added: “I was pretty appalled and sickened by those revelations and that’s why we’ll be re-doubling our efforts to try and get second jobs banned for MPs.”