UK Conservative lawmaker Liam Fox to announce leadership bid on Thursday
A devout Christian, he voted against gay marriage in 2013.
The contest was triggered when Prime Minister David Cameron announced he would resign after the Brexit vote.
In a speech in central London, Mr Crabb uniting the country is his main priority.
“That issue is now settled, we move on from it and I’m absolutely committed to doing my bit to create a tolerant, decent society for everybody regardless of their background, regardless of their sexuality”.
Business Secretary Sajid Javid also said he is running on a joint ticket with Mr. Crabb as treasury chief.
Mr Crabb was first elected to Preseli Pembrokeshire in 2005.
Mr. Crabb is less well-known to the British public than his expected rivals in the leadership race.
“I think there’s a few really, really competent and impressive people who demonstrate warmth as well as intelligence and I think that’s quite important in politics”, she said. I managed to do that – I brought together people around the table and we’re taking forward a Bill to implement that.
Elsewhere, Health Secretary Jeremy Hunt has hinted that he may run in the contest and Andrea Leadsom, the Brexit backer and former city minister, could boost Johnson’s campaign after having a strong European Union referendum campaign.
But Mr Crabb and Mr Javid positioned themselves as the “blue collar” alternatives to Old Etonian Mr Johnson.
‘A United Kingdom without Scotland is not the United Kingdom; a Great Britain without Scotland is not Great Britain.
“But what I want to do now is start making an argument as to what we do next as a country”.
Asked on LBC Radio whether he was planning on announcing his candidacy before Thursday’s noon cut-off time, he replied: “I will”.
It is expected former London Mayor Boris Johnson and Home Secretary Teresa May will also stand in the contest.
The Work and Pensions Secretary has the support of Attorney General Jeremy Wright and children’s minister Edward Timpson as well as a handful of Tory backbenchers for his leadership campaign.
Stephen Crabb is the dark horse in this race but he knows that the history of Conservative leadership elections tells us that outsiders often win. I am under no illusion that this is a tough challenge, but I believe that Stephen Crabb is the right person to lead us through this hard period and in the years to come.
He said the message from voters in last week’s referendum was that they wanted to take back control of immigration – a “red line” in the negotiations to take Britain out of the EU.
Crabb is viewed as an outsider when compared with Boris Johnson or Theresa May, though Conservatives have often chosen the less obvious candidates for leadership, such as David Cameron when he was up against Tory veteran David Davis.