The Conservative MP for Preseli Pembrokeshire is supporting the Home Secretary Sajid Javid, a friend who he stood alongside on a joint ticket for the leadership in 2016 when Cameron resigned after the EU referendum, agreeing that Javid would be chancellor if Crabb won.
The pair pulled out of the race and Crabb then backed Theresa May.
This time, Crabb told Premier's News Hour that he and Javid hold similar views on One Nation Conservatism and that Javid's background would bring a unique perspective to help the Conservatives "be a more effective party in the 21st century".
Crabb admitted that any leader would find it difficult to negotiate Brexit but that the first challenge was for the potential Prime Minister was to stick firmly to the policies and passions they started with.
He explained: "There'll be a lot of pressure on them to offer jobs to certain colleagues. Don't forget, at this stage of the contest, it's all about getting the votes of individual MPs and there'll be MPs asking for certain jobs or certain favours for lending candidates their votes.
"There'll be pressure on the candidates to make commitments, either funding commitments, or announce different priorities. And I think what's really hard is to keep your own mind and to be your own person.
"I think if you are looking for a practical prayer suggestion, it's for wisdom and strength for the candidates to be their own people and to let their own values and personality shine through when they're being pulled in so many different directions."
When asked what he thought of Boris Johnson's notable absence, Crabb said: "Well, I said last week that, in my view, he should be there. This is both an internal Conservative Party argument that's going on at the moment - picking out a new leader - but it's also, don't forget, picking a Prime Minister for the whole United Kingdom and my feeling is that a lot of communities, a lot of people up and down the country feel probably shut out from this process because they don't get a vote in it.
"They're not members of the Conservative Party and so actually having these TV debates and hustings events is a really important way of connecting this internal Conservative Party process with the wider public in the wider community. So, I felt that all of the candidates should have been there, but he made his choice and he'll probably be feeling today that he did a good job of avoiding the debate given how messy it got in places."
Speaking about whether he thought candidates had stuck to their 'Clean campaign pledge' to not speak ill of other candidates' personalities, he commented: "Yeah, broadly. It's difficult, isn't it? Because when does raising legitimate questions and making what you might feel are legitimate criticisms, when does that stray into the bounds of not conducting a non-clean campaign and not speaking ill of each other? There needs to be a robust conversation otherwise it's not a real contest and it's right for the individual candidates to challenge each other on some of the weaknesses of their arguments or the weaknesses of their particular priorities.
"But what you don't want to see is insults, you don't want to see malign behavior and I think so far we haven't seen any of that."
Sajid Javid, who got 23 votes in the first round, will need to secure 33 votes on Tuesday to stay in.
Speaking about who he would support if Javid doesn't get through, Crabb said: "Well, I'm hoping he will get through the next round and stay in the contest but I haven't given any consideration to who would be a plan B. I'm supporting Sajid because I believe in the man, I believe in his vision and so long as he's in the contest I'll be focused on giving him my hundred-percent attention and support."
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
