The U.S. dollar index, which measures the greenback's strength against a trade-weighted basket of six major currencies, was steady at 95.86.
There was caution ahead of Fed Chair Yellen's congressional testimony on Wednesday with expectations overall that she would maintain a confident tone and expect to continue the process of gradual policy normalisation.
Investors will be looking at second-quarter earnings reports on Friday from big USA banks including JPMorgan Chase, Wells Fargo and Citigroup.
Largely ignored in the Fed report is the debate over fiscal policy, and in particular whether the Trump administration will be able to convince Congress to lower taxes and increase infrastructure investment, and if so, the impact of such stimulus on the economy.
Tokyo's benchmark Nikkei 225 index gained 0.57 percent, or 114.50 points, to 20,195.48, while the Topix index of all first-section issues advanced 0.72 percent, or 11.66 points, to 1,627.14.
Stock futures in the USA for Monday were up, suggesting shares on Wall Street will open higher and extend gains that were made following the release last Friday of the jobs report by the Labor Department. Barclays bank also cut its 2017 and 2018 Brent forecasts to $52 a barrel.
The strength of the Canadian dollar since early May - it's up more than 6% against its USA counterpart - has been driven by increasing expectations that the Bank of Canada will join the Fed as the second major central bank raising interest rates as the economy continues to expand rapidly.
A rate rise from Canada's central would be its first interest rate rise in almost seven years.
In Europe, the Stoxx 600 Index ended the day with a 0.4 percent gain from the previous close.
"Normalization of monetary policy in the coming months is nearly priced in, and the Fed will start shrinking its balance sheet in September, and this does not necessarily mean a delay of rate hikes", said Masafumi Yamamoto, chief forex strategist at Mizuho Securities in Tokyo.
Bank of Japan is not taking any steps to make Yen stronger, experts say!
BONDS: Bond prices were little changed.
USA crude oil -0.2% at $44.31/bbl. In early trades, the local unit was trading at US$0.7605, up from US$0.7603 on Monday.
"We have been emphasising the fundamental weakness of the South African macro story for some time, and believe that market pricing on ZAR (the rand) showed a degree of complacency that in part was explained by low G3 bond yields", analysts at Morgan Stanley wrote in a note.
The 10-year U.S. Treasury yield was steady near a two-month high of 2.398 percent hit on Friday.