Hundreds of thousands of petroglyphs, or rock carvings, dating back to the last Ice Age, are estimated to be at the site in the state’s north.
But Woodside wants to place a large onshore facility on the peninsula, the former Dampier Island, to support its gas production.
Interest groups are waiting on Senator Campbell to make a decision on whether some of the petroglyphs can be sacrificed to make way for the facility.
But he spoke about Burrup today while releasing details of a planned overhaul of Australia's main environment protection act.
"There will be, by the expansion of Woodside's operation, some disturbance to some rock art," he told reporters.
"But the great majority of it will be undisturbed and I want to make sure the great majority of it has a world-class, long-term, 30- to 40-year management plan in place that protects it, better than it ever protected it before."
Senator Campbell said that, in considering whether to protect or allow the development to proceed, he had to consider the positive impact of LNG on global warming issues.
"If you put unnecessary impediments in the way of LNG development in the Burrup, you are unnecessarily delaying the world's response to climate change," he said.
"It's one of the important reasons why the Burrup development must go ahead."
Greens leader Bob Brown said this claim was fatuous.
"(Under the planned new environment laws), the Burrup, which ought to be protected in its entirety, will be a first casualty of this process.
"The Burrup ought to be nominated for world heritage," he said.