Mr Corbyn faces a leadership contest following this week's challenge by former shadow business secretary Angela Eagle.
Britain's opposition Labour Party has ruled current leader Jeremy Corbyn has the automatic right to stand in a new leadership contest.
"I put to him a series of alternatives as recently as two days ago - they have been rejected".
Following the European Union referendum, 172 Labour MPs indicated they had no confidence in their leader, and only 40 MPs gave Mr Corbyn their backing.
On Tuesday evening the National Executive Committee voted by 18-14 that Corbyn would automatically be on the ballot - which is lucky for him as there is a good chance he would not have secured the necessary MP votes otherwise.
Speaking outside Labour HQ, Mr Corbyn said: "I am sure Labour MPs will understand and come together in order to present to the British people the option of a different and better ways of doing things". Join as a registered supporter.
"But if there is yet to be a leadership contest, let it be conducted in a comradely manner and we at the TSSA look forward to supporting Jeremy continue to develop and expose his positive programme for the next Labour government".
The leadership contest was triggered on Monday when lawmaker Angela Eagle challenged Mr Corbyn.
A source close to Mr Smith, who is expected to formally launch his campaign on Friday, said: "This has not been an easy decision".
Mr Smith's announcement came amid reports that the NEC has suspended all local Constituency Labour Party meetings until the end of the leadership campaign following complaints of harassment and intimidation.
"I am calling on all Labour Party members and supporters to act with calm and treat each other with respect and dignity, even where there is disagreement".
Ms Eagle has struggled to overcome her voting record, including support for the Iraq war in 2003 and for bombing Syria past year. "But I hope and I expect it will be me", he said.
"The Labour Party, the party of equality who pioneered anti-discrimination - it's about time they had their first elected woman leader". It means more than 100,000 people who have signed up since then will not be sent ballot papers.
It is likely the victor will be announced at the party conference in September.
Corbyn said the incident was "extremely concerning" and, as someone who has himself received death threats in recent weeks, condemned the threatening behavior.