China’s top envoy in Australia has extended the olive branch to Peter Dutton’s Coalition, urging the major parties not to let “differences” between the two countries “hijack our cooperation”.

At a press briefing in Canberra on Tuesday, the ambassador, Xiao Qian, said Beijing was “happy” with the diplomatic stabilisation between Australia and China under Labor – but “not complacent”.

The ambassador said he was looking to move the relationship beyond stabilisation and further into “development”.

“We have common grounds. We have differences. We even have disputes on certain issues,” he said.

“But for a mature relationship between two countries, we will always focus on our common grounds … we will manage the differences so that those differences are not going to disrupt too much, or to define, or to hijack, the overall relationship.”

Ties between Australia and China broke down under the former Coalition government after the former prime minister Scott Morrison backed an international inquiry into the origins of the Covid-19 virus.

Australia was hit with trade sanctions on exports to China and frozen out of minister-to-minister dialogues.

While the once-strained relations have since stabilised, there are still points of contention on territory disputes in south-east Asia, Taiwan, China’s ties to Russia and human rights abuses in Xinjiang and Tibet.

Dutton has not been shy when it comes to criticising China in the past but has taken a different approach in recent months.

Dutton even went as far as calling himself “pro-China” in June during Premier Li Qiang’s visit to Australia.

When asked how China was preparing to deal with a potential Dutton government after the next federal election, Xiao said he would seek to show China wanted to maintain a good relationship with Australia.

“This is important to our two countries that we manage the differences in disputes wisely, wisely, in a sense that you don’t allow the differences to hijack our cooperation, because that’s not going to serve our respective national interests,” he said.

Xiao said he had met with Dutton and the shadow foreign affairs minister, Simon Birmingham, and there was “ongoing engagement”.

In October, Birmingham told ABC radio there was concern over whether China believes “Australia will stand as strongly in relation to identifying and speaking about those security concerns and risks in the region”.

“I believe, and we believe that Australia should,” he said.

In June, Birmingham told Guardian Australia he would be “predictable” and “transparent” in his approach with China, conceding the Morrison government’s megaphone diplomacy was counterproductive.

Both countries are awaiting the details of Donald Trump’s pledged tariff on Chinese goods, which the treasurer, Jim Chalmers, already warned could have flow-on effects for Australian exporters.

On Tuesday, the president-elect said he would place an “additional 10% tariff” on Chinese imports, after initially floating a 60% tariff.

Xiao said “there’s no reason for [Australia and China] to compromise our respective national interests for the sake of a third party”.