The member for the Darwin-based seat of Solomon was charged on Thursday over allegations he assaulted NT Administrator David Connolly earlier in July.
Gosling, 54, did not comment as he left Palmerston Police Station after being charged with two counts of assault.
Nationals senator Bridget McKenzie said he should stand aside from his role as special envoy for defence, veterans' affairs and northern Australia until legal proceedings had concluded.
"It's an important part of our democracy of keeping integrity within our Westminster system that the prime minister does do the right thing and stand Mr Gosling aside until his name is cleared or until the matter is dealt with in court," Senator McKenzie told News 24.
Liberal senator James Paterson on Thursday also said he hoped Gosling would move aside.
Gosling is due to appear at Darwin local court on September 1. He has denied the allegations.
The attorney-general Michelle Rowland would not be drawn on whether her colleague should move aside from his role.
"As you can appreciate, because the matter is before the court, I'm limited in what I can say," she told Channel Nine.
"The commentary around this matter needs to be handled very seriously."
Northern Territory senator Malarndirri McCarthy told ABC Radio she was upset by the news, as she had found Gosling to be a "very good and decent person".
She said conversations about whether he should step down would need to be between Gosling and the prime minister.
The alleged incident reportedly occurred at the NT Thailand Grand Festival in Darwin on July 18, with Gosling posting photos from the event on social media that day.
Gosling, a retired army officer who has represented Solomon since 2016, released a statement after his arrest.
''These are ridiculous allegations that I categorically deny," he said in the statement.
"I've had no dealings with the administrator since congratulating him following the announcement of his appointment late last year."
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