US President Barack Obama has wrapped up a state visit to Japan during which he assured America's ally that Washington would come to its defence.

But the two countries failed to clinch a trade deal key to both his "pivot" to Asia and Prime Minister Shinzo Abe's economic reforms.

Mr Obama and Mr Abe had been seeking to show the alliance was strong in the face of a rising China.

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But their success in putting recent strains behind them was partially marred by a failure to reach a deal that is seen as crucial to a broader regional trade pact. That failure delayed a joint statement on security and economic ties until shortly before the US leader left for Seoul.

South Korean is the next stop on his week-long, four-nation Asian tour. Mr Obama and Mr Abe had ordered their top aides to make a final push to reach a trade agreement after the leaders met on Thursday.

But Economy Minister Akira Amari told reporters that gaps remained despite recent progress.

"This time we can't say there's a basic agreement," Mr Amari told reporters after a second day of almost around-the-clock talks failed to settle differences over farm products and cars.

"Overall, the gaps are steadily narrowing."

Putting a positive spin on the trade front, the two sides said in their ­statement that they were committed to taking "bold steps" to reach a two-way deal, which would inject momentum into a delayed 12-nation Trans-Pacific ­Partnership (TPP) trade pact.

A senior US trade official said the two sides had achieved a breakthrough on market access, but provided few details.

"There are still details to be worked out," said the senior official accompanying Obama to South Korea.

"There is still much work to be done ...

"We believe we do have a breakthrough in our bilateral negotiations."

The TPP is high on Abe's economic reform agenda and central to Obama's policy of expanding the US presence in Asia.