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MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.2%, with Seoul putting on 0.4%. Japan's Nikkei rose a modest 0.2% after several sessions of losses.
European markets had calmed on Friday as investors decided that losses associated with the founding family of Banco Espirito Santo were unlikely to disrupt Portugal's financial system or revive broader worries about the bloc's weaker economies.
The S&P 500 EMini contract was trading up 0.1% on Monday, after the cash index ended with similar gains on Friday. The Dow closed up 0.17%, while the Nasdaq added 0.44%.
Attention will be on shares in Citigroup, which sources said would announce on Monday a deal to pay $7 billion to resolve a US government investigation into shoddy mortgage-backed securities.
Many of the major banks report earnings this week, along with big tech names including Intel Corp, Yahoo Inc, eBay Inc and Google Inc.
Federal Reserve Chair Janet Yellen's two-day appearance in the US Congress from Tuesday will dominate global markets, which want above all to know how long rates might stay near zero once the central bank ends its asset-buying programme.
The futures market rallied sharply last week as investors again pushed out the likely timing of a rate hike into the second half of 2015.
Data from the US this week includes retail sales, industrial production and several housing indicators.
China watching
In Asia, China reports gross domestic product (GDP) for the second quarter on Wednesday, along with other data including retail sales for June.
Analysts estimate the Chinese economy grew 7.4% compared to the same quarter last year, and anything less than that would likely unsettle markets.
The Bank of Japan concludes a two-day meeting on Tuesday and might have to trim its growth forecasts in the wake of disappointing second quarter data.
European Central Bank President Mario Draghi will speak at the European Parliament later on Monday while the EU 28 Summit on Wednesday will see Jean Claude Juncker confirmed as EC President.
Bank of England Governor Mark Carney and his deputy Andrew Bailey face questions from the British parliament on Tuesday, while jobs figures the day after will influence the outlook for interest rates.
Currency markets were quiet on Monday with the dollar index steady around 80.209, a level it has gravitated towards since recovering from a two-month low of 79.740 on July 1. The euro bought $1.3603, having stuck to a tight range around $1.3600 for over a week now.
Against the yen, the greenback fetched 101.37, holding off a seven-week trough of 101.06 plumbed last Thursday. The euro was near 138.00 yen, recovering from last week's fall to a five-month low of 137.50.
Gold was a shade firmer at $1,338.40 an ounce, not far from a 3-1/2 month high of $1,345 reached last week. Prices for the safe haven metal have been supported in part by the intensified fighting in Gaza.
Yet oil markets seem to have become less concerned that the violence in the Middle East would affect fuel supply in any major way, pulling prices steadily lower.
Brent crude oil was a cent firmer at $106.67 a barrel and just off a three month-trough of $106.27. US crude added 2 cents to $100.85 per barrel.
