BEIJING (Reuters) - China has invited Japanese Prime Minister Shinzo Abe to visit the country at a time convenient for both sides, its foreign ministry said on Thursday, as the neighbours step up efforts to improve frayed relations.

The two countries have sparred frequently about their painful history, with China often accusing Japan of not properly atoning for invading its neighbour before and during World War Two.

Ties between the world's second and third-largest economies have also been clouded by a long-running territorial dispute over a cluster of East China Sea islets and suspicion in China about Abe's efforts to amend Japan's pacifist constitution.

More recently, however, the two have sought to improve ties, with Abe and Chinese President Xi Jinping meeting last November on the sidelines of a regional summit in Vietnam, while Japan's foreign minister visited China in January.

"Diplomatic authorities of the two countries are maintaining communication on this issue," Foreign Ministry spokesman Lu Kang told a daily news briefing, referring to the invitation to Abe.

Both sides should meet each other halfway to create a favourable environment for the trip, Lu added, without elaborating.

(Reporting by Ben Blanchard; Editing by Clarence Fernandez)

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