"I'll make the announcement on my own candidacy at the appropriate time. I think this is the day to remember Theresa May — her duty, her sense of public service, the fact that she has done an incredibly difficult job with enormous integrity," Hunt told his local newspaper, Farnham Herald.
May said earlier in the day that she would step down as the party leader on 7 June but remain prime minister until a new party head was elected.
According to a statement by the Conservative Party's chairman, nominations for the leadership will close in the week starting 10 June. After that MPs will have to narrow the number of candidates down to two by late June so that party members can make their choice before the summer parliamentary recess.