The leadership contenders will take part in hustings and debates in a bid to get grassroots support.
The pair emerged as the final candidates after Ms Truss overturned a narrow lead held by Trade minister Penny Mordaunt, at one point the favourite, to secure the backing of 113 Tory MPs to Ms Mordaunt's 105.
Polls currently suggest Foreign Secretary Ms Truss, who has criticised Mr Sunak for raising taxes during his time as chancellor, is the favoured candidate of the membership.Writing in the Daily Mail, Ms Truss said "the central issue at the next election is going to be the economy" and "we have been going in the wrong direction on tax".
In the Daily Telegraph, Mr Sunak wrote that he believed in "hard work, family and integrity", adding: "I am running as a Thatcherite, and I will govern as a Thatcherite." Speaking on BBC Newsnight, Tory MP Simon Hart, who is backing Mr Sunak, said: "Some people have just a little bit of value added, a little bit of something extra.
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