Stocks were already hurt by a sharp sell-off in commodities and concerns about the outlook for growth in China following weak economic data.
Japan's stock market fell almost two percent, while South Korea's Kospi and Australian shares also dropped, as did oil and gold prices.
In the US, markets closed lower after the blasts accelerated a sell-off started by weak economic data.
Tuesday's falls added to losses seen on Monday following news of a slowdown in China's economic growth in the first quarter of the year.
That news sparked a sell-off in commodities, which then fuelled the selling in global stock markets.
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