Foreign Minister Julie Bishop has played down apparent tensions with her Chinese counterpart, who took aim at Australia's new espionage laws following a meeting between the pair.

Chinese State Councillor Wang Yi said Australia must do more to boost mutual trust rather than being "groundlessly suspicious" after sitting down with Ms Bishop in Singapore at the weekend.

"I know that the line that the media pick up might be the negative line, but the whole discussion was very positive," Ms Bishop told Sky News on Tuesday.

"He also said there's more we can do, and I agree both Australia and China can do more to strengthen and deepen our relationship."

The pair spoke about the use of weapons in the South China Sea, the threat posed by North Korea, and working more closely together in the Pacific during their 45-minute meeting.

Ms Bishop is now looking to organise dates for a visit to Beijing, hoping to join Wang Yi on a morning run through the Chinese capital.

Relations between the two nations soured last year when Prime Minister Malcolm Turnbull accused China of meddling in Australia's affairs - a claim Beijing vehemently denied.