He said: "I have not stopped party meetings taking place, and I actually think that is a mistake".
Responding to a journalist who described him as normal, Mr Smith took the phrase a compliment, and replied: "I am normal".
For me that means a Labour government doing traditional Labour things: investing in our communities, investing in public services, investing in the infrastructure we need - schools, hospitals, new roads.
Mr Corbyn called for the contest to be a debate about the party and the country and said he wanted it to be an example of "vibrant political discussion ".
"I think we have to have the person who is most likely to beat Jeremy Corbyn and I think that's me", said Eagle while sitting alongside Smith on the same programme. Get more Spectator for less - just £12 for 12 issues. "Let us get behind him, and walk tall in solidarity.".
"And if it is not going to reduce those inequalities, then we in the Labour Party should not do it".
Since she announced her intention to run against Mr Corbyn, Ms Eagle has drawn vitriolic responses from some Corbyn supporters.
On Friday a man was arrested after allegedly making threats to kill her.
Mr Smith has vowed to drop out of the race if he secures fewer nominations from MPs than Ms Eagle, but she has not made a similar promise. "This is not an acceptable way to behave in our democracy".
Trade Union Congress leader Frances O'Grady insisted that "now is the time when all working people must stand together" following the EU referendum that has seen a "radical racist right" emerge.
Reuters 4 Theresa May touched down in Berlin for opening talks with Angela Merkel on the UK’s exit from the EU
"I won't be stopped or cowed".
Labour's general secretary last week suspended routine constituency and branch meetings until after the leadership election amid reports of intimidation and threatening behaviour.
He offered to withdraw if Ms Eagle managed to get the greater number of nominations.
"They understood what Labour was for".
Ms Eagle borrowed Theresa May's famous 2002 description of the Conservatives as she called for action from the Labour leadership on "abuse, misogyny, homophobia (and) anti-Semitism" affecting the party. But she believes that she is better qualified because of her experience as a government minister, and that it is time for Labour to elect a woman leader.
Anyone wanting to vote on the new leader will have just two days this week to sign up and have to pay £25 compared to £3 a year ago.
"The party has always championed equality, but it's important that we put our money where our mouth is", adding that she felt she would be "an effective leader".
"We need more than posturing, we need more than sloganising".
"I'm hoping there will be an understanding that it's simply not very fair to say to people that joined the party in the last six months that "Sorry, your participation is no longer welcome, because we're having a leadership contest".