Mark Pritchard, Christian and Conservative MP for The Wrekin, told Premier the Conservative leadership battle will be a short race.
A new Conservative leader should be in place by September 2nd, the party's 1922 Committee executive has recommended - with nominations opening on Wednesday and closing at noon on Thursday.
He said: "It'll soon be over very, very quickly.
"What's needed is someone who's going to be a political healer, to bring the country together, the party together and who will reassure the international markets.
"Somebody's who's confident and able to navigate this complex and challenging path that this country has chosen for itself."
He added: "We'll have to wait and see who that is."
Boris Johnson and Teresa May are two names that have been associated with the race.
Mr Pritchard told Premier the candidates he wants to see need "vision for the country, values and recognise that they need to bring the country together again".
He said that it was important that the new PM maintained a "positive" relationship with the EU as well.
Earlier, an emergency Cabinet meeting agreed that a new team should be set up to assess the fallout from Friday's referendum result.
Additionally, after the Chancellor George Osborne has been heavily criticised for not speaking sooner, Mr Prichard told Premier's News Hour that George Osborne was right to wait to make a speech.
He said: "The Chancellor wasn't in hiding, he was on the phone to treasury secretaries and finance ministers around the world.
"I think it's right that these big decisions are thought through and decisions made in haste aren't usually worth much.
"I think if he rushed out ten minutes later and spouted off things that hadn't been thought through you might be criticising him for that."
He went on: "I think it was right that the Chancellor took time to reflect and think through, and hold discussions privately with the Bank of England, to ensure that any response was not only in the national interest, but also was trying to steady the markets elsewhere around the world."
Listen to Premier's Antony Bushfield speak to Mark Pritchard here:
