Australia and New Zealand have been at loggerheads in recent months, trading barbs over the 2021 format for Super Rugby and the scheduling of the four-nation Rugby Championship that will see the All Blacks spending Christmas in quarantine if their final game is played on December 12.
The breakdown in relations has come amid financial pressures due to the Covid-19 pandemic and uncertainty over the future of southern hemisphere competition following South Africa's decision to pull teams from Super Rugby.
"There is respect there but the relationship is at probably the lowest ebb it's ever been at," McLennan told New Zealand broadcaster Sky Sports.
"But I'm trying my hardest to fix that over time. I think the fundamental issue from us is that (New Zealand) have got to respect our position."
McLennan said Australia had been "greatly offended" when New Zealand Rugby announced mid-year it planned to organise a 2021 tournament involving its five Super Rugby teams without consulting its southern hemisphere partners.
He said Australia were willing to regard that as "water under the bridge", however, and were committed to forming a trans-Tasman competition with New Zealand.
"I think Covid's throwing up a whole lot of issues, I'm not sure where that's going to land but, ultimately, we've got a really powerful Anzac (Australia and New Zealand) block that we should be leveraging, working together," he said.
"We've got to work together to see how we leverage our strength on the global stage.
"Money's tough at the moment and that's why we've got to get the TRC (Rugby Championship) away.
"We're just going to battle our way through it."
New Zealand Rugby chief executive Mark Robinson dismissed McLennan's comments as "a bit of bluster", and said RA had invited he and NZR Chairman Brett Impey to Australia during the Novemver 7-December 12 Rugby Championship.
"Clearly (RA) have a strategy and narrative that they want to portray," he told reporters in a video call on Thursday.
"We don't operate like that but respect if they want to. We will carry on engaging about the future opportunities with them and will just have to largely get on with our own business and ignore some of the things that are said like that.
"We have got a game that is battling for survival at all levels."