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U.S. consumer inflation figures for June are due on Tuesday while retail sales, a key gauge of consumption, are released on Thursday.
The U.S. corporate earning season will start this week, providing another window to assess the scale of the damage as well as the recovery, from the pandemic.
"I expect stock markets to remain firm and the dollar to slightly weaken, but everybody is getting nervous about a possible correction," said Kazushige Kaida, head of FX Sales at State Street Bank and Trust's Tokyo Branch.
The euro rose 0.25% to US$ 1.1329, maintaining its slow uptrend since late last month. Looming large for the common currency was a planned EU summit on July 17-18, where leaders need to bridge gaps on long-term budget and economic stimulus plans.
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European Council President Charles Michel proposed a smaller joint EU budget for 2021-27 than previously envisaged to placate thrifty countries in the north.
The British pound also gained 0.3% to US$ 1.2656, edging near its three-week high of $1.2668 touched last week.
The Australian dollar added 0.3% to US$ 0.6969. The dollar also lost small ground against the safe-haven yen, to 106.83 yen, staying near two-week lows of 106.635 set on Friday.
Investors also looked to China, where economic recovery is gaining momentum as the outbreak has largely been contained.
China will release its June trade data on Tuesday and a batch of other data, including second quarter GDP, on Thursday. The Chinese yuan gained 0.15% to 6.9987 per dollar in early trade.
