Mr Corbyn will use a speech on Wednesday to outline his plans to “renationalise” the NHS.
Meanwhile, Owen Smith has promised to attempt to block the triggering of formal negotiations to leave the European Union until Theresa May promises a second referendum or general election on the terms of the final Brexit deal.
The announcements come after the leadership race took a dramatic turn on Tuesday evening when Mr Smith appeared to describe Mr Corbyn as a “lunatic” at an event in Hammersmith.
The Pontypridd MP told party members: “What you won’t get from me is some lunatic at the top of the Labour Party.”
Allies of Mr Corbyn called for Mr Smith to retract his remarks and apologise to people suffering from mental illness.
But Mr Smith has now sought to clarify his comments, insisting he was not talking about his rival.
He told the BBC Radio 4 Today programme: “I was saying that I wasn’t a lunatic.
“Having been accused earlier in the evening of running around like a lunatic, I was saying I wasn’t a lunatic, but if anybody’s offended by the use of that word then I do apologise and I’ve done that already this morning and I’ll do it again.
“But I wasn’t talking about Jeremy. I was talking about me.”
Mr Smith has said that, under his leadership, Labour would vote against triggering Article 50 - the mechanism which opens the door to the UK leaving the EU - until the Government commits to a second poll.
He said: “I’m a passionate pro-European and I will fight tooth and nail to keep us in the EU.
“Under my leadership, Labour won’t give the Tories a blank cheque. We will vote in Parliament to block any attempt to invoke Article 50 until Theresa May commits to a second referendum or a general election on whatever EU exit deal emerges at the end of the process. I hope Jeremy will support me in such a move.”
Meanwhile, Mr Corbyn is due to set out his NHS policies with commitments expected to include ending private finance initiative (PFI) contracts and guaranteeing bursaries for nurses.
He is expected to say: “The Tories have run our treasured National Health Service into the ground and we need to get serious about stopping them.
“The next Labour government would go further than reversing Tory cuts - it would deliver a modern health and social care service that is fully publicly provided and fully publicly funded.”
Mr Corbyn became embroiled in a row with Virgin Trains on Tuesday after CCTV images released by the company appeared to show the Labour leader walking past empty, unreserved train seats before he was filmed sitting on the floor complaining about “ram-packed” carriages.
Mr Corbyn then apparently found an unreserved seat to sit in as he travelled on the three-hour 11am Virgin Trains service from London King’s Cross to Newcastle on August 11.
Sir Richard Branson, who co-owns Virgin Trains with Stagecoach, got involved in the row, posting a link to the CCTV images on his Twitter account.
Mr Corbyn’s campaign team said he was unable to find unreserved seats for his group so he sat with other passengers in the corridor and seats became available later in the journey.
But Virgin Media said it was “puzzled” by the suggestion Mr Corbyn was unable to find unreserved seats when he boarded the train because CCTV images appeared to show “they’re right next to him”.
The winner of the Labour leadership contest is due to be announced on September 24.