Health Secretary Matt Hancock, former Brexit secretary Dominic Raab, international development secretary Rory Stewart and Home Secretary Sajid Javid have agreed to not "speak ill of fellow Conservatives".
In the hope of unifying their party, the Tory leadership contenders have also pledged to "not engage in personality attacks on others" and "stick strictly to the spending limits".
Christians in Politics launched a similar campaign 'Disagree Well' before the EU referendum, which urged people to consider their approach to political division.
Speaking to Premier, Christians in Politics executive director, Andy Flannagan said: "It's all very well to talk about disagreeing well, it's all very well to try and be more polite in our public discourse.
"But actually, you can only really truly disagree well, if you're building good relationships with people that will allow you to disagree well."
Andy said this shouldn't prevent the public knowing the character of a potential leader.
"To talk about the character of our leaders is really important, but I think there are ways of doing that," he said.
"And there are humble ways of doing that in a way that doesn't necessarily take someone down."
Following Theresa May's announcement to resign as Prime Minister on Monday, there are currently eleven contenders in the Tory party leadership contest.
Christians in Politics hopes the 'clean campaign' will promote honest and open debate as respectful relationships are established between candidates.
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