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The Manila-based bank said the region's gross domestic product was projected to expand 6.6 per cent in 2013 and 6.7 per cent in 2014, from last year's softer performance of 6.1 per cent.
"Developing Asia is bouncing back from the slowdown in the previous year," said the bank's annual Asian Development Outlook report, which covers 45 economies in Asia and the Pacific.
"Robust domestic demand and greater reliance on regional trade will accelerate growth," it added.
A rebound in China and a solid performance in South-East Asia, which was the only sub-region to enjoy faster growth last year, are also contributing to the region's momentum.
But the report warned that political risks linked to wrangling over the US debt ceiling, fatigue over tough austerity measures in the eurozone, and long-simmering tensions over border disputes in Asia could threaten the outlook.
It added that, since stronger economic activity could spur renewed price pressures, governments must monitor inflation, which was projected to rise to to 4 per cent in 2013 and 4.2 per cent in 2014, from 3.7 per cent in 2012.//DPA