They followed gains in Asia, where MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.3 percent and Japan's Nikkei gained 0.8 percent to a one-week high, helped by weakness in the Japanese currency.
Gold prices hovered near four-month lows on Tuesday and the dollar held firm on expectations of tighter US monetary policy as the market awaited a speech from Federal Reserve Chair Janet Yellen this week.
Chair Janet Yellen will submit Federal Reserve's semi-annual Monetary Policy Report to Congress on Wednesday.
Against the yen, the dollar was 0.1 percent higher at 113.98, after notching a high of 114.18 in the wake of the jobs report, its loftiest level since May 11.
Data on Monday showed exports from Germany, Europe's biggest economy, rose more strongly than expected in May.
"Looking ahead, we think improving corporate earnings are the key ingredient needed to sustain the equity bull market", said Bob Doll, senior portfolio manager and chief equity strategist at Nuveen Asset Management Llc.
At a press conference last month, Yellen said the normalization of Fed's balance sheet could start "relatively soon" if the USA economy evolves in line with their expectations.
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The dollar rose nearly 0.4 per cent to 114.29 yen, a two-month peak, while the dollar index - which measures the dollar's value against a basket of other major currencies - was a touch firmer at 96.071.
CURRENCIES: The dollar fell to 113.84 from 114.05 yen late Monday.
The Canadian dollar fell against its U.S. counterpart as oil prices fell and traders await an interest rate hike decision by the Bank of Canada on Wednesday.
"By contrast, the Bank of Japan is nowhere near a policy exit, and it's taking steps that weaken the yen", he said.
International Container Terminal Services was among the biggest gainers on the index, climbing as much as 2.6 percent, after signing an agreement with a dredging company to deepen the Congo River in Africa, a move that would realise cost savings for the terminal operator from 2018.
On Friday, the BOJ sought to keep Japanese government bond yields near its policy target, embarking on a special market operation as well as increasing the size of its regular JGB purchase operations. The latest USA economic reports, particularly for jobs, have been upbeat.
The report also noted that long-term nominal U.S. Treasury yields have declined and remained quite low by historical standards since the beginning of the year, largely reflecting "declines in inflation compensation" due to soft inflation data.
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