The leaked draft deal between the two nations would allow for Chinese ships to be based in the Pacific, as well as have a navy base less than 2000 kilometres off Australia's coast.
In a joint statement Foreign Affairs Minister Marise Payne and International Development Minister Zed Seselja said Australia respected the right of every Pacific country to make sovereign decisions.
But the Australian government was concerned about actions that could undermine the stability and security of the Indo-Pacific region, they said.
Australia will allocate $22 million in the upcoming budget for the Solomon Islands government to fund salaries for essential workers to help with the impacts of civil unrest and COVID.
China is so far remaining tight-lipped about the draft deal.
A foreign ministry spokesman told Reuters reporters on Friday China backs the Solomon Islands in upholding social order, when asked if the two nations were in talks on a security partnership.
At a regular media briefing in Beijing, ministry spokesman Wang Wenbin did not confirm or deny the proposed cooperation when asked about it.
Meanwhile, New Zealand Foreign Minister Nanaia Mahuta said Pacific partners should be transparent in their actions, Reuters reports.
"Such agreements will always be the right of any sovereign country to enter into, however developments within this purported agreement could destabilise the current institutions and arrangements that have long underpinned the Pacific region's security," she said in a statement.
Mr Morrison said he wasn't blindsided by the deal and Australia was still a leader in the Pacific region through development assistance and investments in telecommunications and infrastructure.
Australia was active in the region to ensure "a free and open Pacific", the prime minister said.
"We share with our Pacific family ... culture, the principles of democracy and freedom, and these are things that are very important to the Pacific island peoples."
Mr Morrison said he had been in regular contact with the Solomon Islands, and indicated he would see how the China-Solomons deal progressed.
Defence Minister Peter Dutton earlier on Friday rejected suggestions Australia had dropped the ball in the region, with some suggesting cuts to foreign aid led the Solomon Islands to align more closely with China.
Despite the deal, Mr Dutton said Australia still had a "fantastic" relationship with the Solomons.
"We want peace and stability in our region, we don't want pressure and exertion from China to continue to roll out in the region," he told the Nine Network on Friday.
The Solomon Islands switched diplomatic ties from Taiwan to Beijing in 2019, which partly led to riots in the capital Honiara in November last year.
Australia, which has historically provided security to the Solomons, led a policing mission after the riots following a request from the country's prime minister, Manasseh Sogavare.
The prime minister said Australia had increased investment in the region by 50 per cent.
Opposition Leader Anthony Albanese said the deal between the two nations would have serious implications for Australia.
"If the reports are correct, then this would have real implications for the region and is of concern," Mr Albanese told reporters on Friday.
"There is a need for the government too, as always, make sure that Australia's interest is represented while, of course, respecting other sovereign nations and their right to make decisions."
The Labor leader said Australia needed to ensure the country was the partner of choice for the Solomon Islands.
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