Demolition of the building that houses The Gods Cafe and Bar at the Australian National University had been scheduled to begin this week as part of the multi-million dollar Union Court redevelopment.

But a Canberra court this week granted the cafe a stay of execution until it could properly hear a dispute about the lease.

The Gods Cafe and Bar owner, Jaye Min, and the ANU have been locked in a legal tussle about the right to end his tenancy.

Mr Min - who had signed a lease for the site until 2018, with the option to extend to 2023 - had been ordered to leave by Tuesday.

Mr Min has defied the orders and instead continued to operate his business - including giving away hundreds of free coffees on Monday - claiming the university has not correctly terminated his lease and has no right to kick him out.

Mr Min's lawyers, Kamy Saeedi Lawyers, argue the university had to give Mr Min six months notice to leave the premises.

A court has previously heard Mr Min had been handed his marching orders in April.

But the ANU argues it can cancel a lease at any time if it has an alternative use for the site.

It also says Mr Min had been aware of redevelopment plans as the proposal has been on the drawing board since 2014.

The $220 million redevelopment includes new teaching and student buildings, a purpose-built events and theatre building, student accommodation, a swimming pool, gym, outdoor spaces and amphitheatre, bars, event pavilions, cafes, services, shops and underground parking.

The university last week threatened to block access to the cafe, shut off the water and power, dispose of the cafe property left inside, and physically take possession of the property.

In a letter from its lawyers, the ANU said it intended to erect hoarding and disconnect services to the site on Tuesday.

The ANU offered Mr Min supervised access to collect personal items on Tuesday, but said it required vacant possession and expected any keys or access passes to be returned on the same day.

The university also offered to waive the usual legal requirements for tenants to "make good" and repair any damage upon departure, as the building is set to be demolished.

But the ANU was forced to back down after an ACT Supreme Court judge on Monday granted Mr Min an urgent injunction to pause demolition.

Associate Justice Verity McWilliam - in reasons yet to be published - found there was a genuine question to be tried as to the correct timeframe to terminate the lease.

The decision means the ANU cannot act on the termination notice until after a hearing, which has been set for later this month.

The ANU had previously claimed any delays in the redevelopment would cost $120,000 per day.

Although, the court heard the pre-demolition work could continue in the meantime.

The matter is set down to be heard on July 19