Ms Nandy's comments come amid amid calls from Ms Long-Bailey for a social housing "building boom".
Ms Long-Bailey has pledged to build hundreds of thousands of new council homes if she’s elected as Jeremy Corbyn’s successor.
However, she also appeared to suggest such issues were less of a priority to her fellow candidates, prompting a curt response from Ms Nandy.
“This is an attempt to manufacture division where there is none. A decent, affordable home is a human right,” the Wigan MP said.
“As Labour leader I would maintain our commitment to a programme of mass council house building and ensuring secure, affordable tenancies for renters.”
Despite her comments, Ms Long-Bailey addressed supporters in Portsmouth on Friday, saying: “There’s not been a lot of talk about housing in this leadership campaign, sadly.
“But the fact is that we’re in a housing crisis.”
She continued: “One fundamental way to change that, to make housing more affordable both for the private sector and to ensure we’ve got enough supply is to build more council houses, at least 100,000 per year.”
Prior to the event, the shadow business secretary’s team said she was urging her rivals to back her commitment to push for a council house “boom”.
Sir Keir Starmer has already backed a large-scale building programme and Ms Nandy shared her own ambition to exceed the party’s manifesto pledge to build 150,000 new council and social homes per year within five years.
She said: “We need to go further than the manifesto, with a plan to tackle the overheated housing market in London and big cities to balance the economy.”
Elsewhere in Ms Long-Bailey’s speech on Friday, she vowed to support whoever is elected in the Labour leadership contest should her own campaign fail.
“Whoever gets elected in this leadership campaign, if it’s not me I’ll support them,” she told supporters.
“I might not agree with everything they do and I might speak to them in private and have a go at them for not adopting all of the policies that I want to adopt but I’ll never criticise them in public because that would not get us into a position where we’d ever win a general election."
Labour members and eligible supporters will begin voting for the new leader and deputy on Monday, with the result to be announced on April 4.