At 0758 GMT, the rouble was 0.4pc stronger against the dollar at 73.34 and had gained 0.2pc to trade at 80.14 versus the euro.
On Tuesday China reported that its March exports fell 6.6pc in year-on-year terms, compared with a forecast for a 14pc drop, and imports fell by less than 1pc, compared with a 9.5pc drop forecast by economists.
China's trade report saw stock markets in Asia and Europe extend their gains and helped risk-sensitive currencies, including the rouble, firm.
"The trend among emerging market currencies, which strengthened moderately this morning, will help support the rouble," Bogdan Zvarich, chief analyst at Promsvyazbank, said in a note. He expected the rouble to move towards 73 against the dollar early in the day.
The mood on global markets was also lifted by news that 10 US governors on the east and west coasts formed two regional pacts to coordinate gradual economic reopenings as the coronavirus crisis in showed signs of receding in the United States.
The rouble in recent weeks has also been buttressed by the Russian central bank's daily sales of foreign currency.
Central bank data published on Tuesday showed it had sold 12.9 billion roubles ($176.41 million) last Friday.
Russian stock indexes were trading slightly higher.
The dollar-denominated RTS index was up 1.2pc to 1,138.8 points, while the rouble-based MOEX Russian index was 0.9pc higher at 2,651.6 points.