The High Court in Brisbane on Thursday ordered the government's lawyers to submit their case by Monday ahead of two June 12 directions hearings for the challenges.

They have been made by outspoken billionaire businessman Clive Palmer and Travel Essence, which is understood to be a consortium of six plaintiffs.

Currently, school students, workers and freight drivers can enter the state without an issue, but Queensland is closed to anyone else because of the COVID-19 crisis.

Premier Annastacia Palaszczuk has previously refused to buckle to pressure to reverse her decision to keep the borders closed, saying she's keeping Queenslanders safe.

She has flagged a potential September re-opening, however, this is under a monthly review and could be pushed forward.

Earlier, Deputy Premier Steven Miles said the state would not be bullied after Prime Minister Scott Morrison accused the Palaszczuk government of ignoring an earlier agreement to open to interstate travel in July.

He said there was no medical advice to support their extended closure.

Mr Palmer's challenge, which was made through his flagship company Mineralogy, could be heard by the full bench as early as June 29.

The Travel Essence challenge is not as far progressed, with Chief Justice Susan Kiefel likely to indicate when it will be heard on June 12.

It is understood to be part of a wider effort to help Queensland's tourism industry recover from the effects of COVID-19.

One Nation leader Pauline Hanson has also threatened legal action in the High Court if borders aren't reopened.

Australian Associated Press