Prime Minister Tony Abbott has defended his decision to visit South Korea and Japan on the same trip, telling his Korean counterpart he could not play favourites in the region.

But he’s stressed Australia wants more than just trade from Korea, because it’s a country that would rather “find friends than pick fights”.

Mr Abbott arrived in Seoul on Tuesday for talks with President Park Geun-hye, and to formalise the free trade agreement struck in December.

His visit follows a two-day stint in Japan, where he and Prime Minister Shinzo Abe finalised a long-sought trade deal and agreed to elevate defence co-operation.

Seoul and Tokyo aren’t on speaking terms, with the legacy of Japan’s wartime rule over Korea and a territorial dispute feeding mutual hostility and suspicion.

Mr Abbott said he would continue to visit Japan and other countries in the region because they were so important economically to Australia.

“I didn’t want to visit any of them, without visiting all of them,” he said of this first official trip to North Asia.

“It’s very important for me to show suitable respect to the countries that take our exports and provide us with so much of our prosperity.”

South Korea, like China, is notoriously sensitive about Japan and suspicious of its desire to bolster its presence in the region.

Mr Abbott told a Japanese business lunch this week that his decision to stop in Japan first before venturing elsewhere in the region “was a deliberate statement of my government’s priorities”.

He will spend a little over a day in Korea, compared to two days in Japan and three in China.

But he used his meeting with President Park to show Australia takes Korea seriously, announcing a “vision statement” on defence co-operation.

Mr Abbott said both nations trusted each other, exemplified by a joint amphibious military exercise currently under way with Korean soldiers.

President Park also thanked Mr Abbott for supporting Seoul’s desire to reunify the Korean Peninsula, still separated 60 years after the end of combat.

She also expressed a desire to boost defence technology links between Australian and Korean military companies.

AAP