The dollar changed hands at 78.37 yen in Tokyo afternoon trade against 78.48 yen in New York late Thursday.
The euro bought $1.3015 and 102.00 yen, compared with $1.3018 and 102.16 yen in New York.
The Japanese unit rose after the BoJ said its policy board had voted unanimously to keep rates at between zero and 0.1 percent, while it has left an 80 trillion yen ($1.02 trillion) asset purchase programme in place.
"Expectations were not huge, but there are few, especially non-Japanese investors, that were expecting new easing measures from the BoJ," UBS head of FX Hiroshi Maeba told Dow Jones Newswires.
Yuji Saito, director of foreign exchange at Credit Agricole in Tokyo, also said: "The majority of us are already expecting that the BoJ will take fresh easing measures by year-end."
The euro was steady against the dollar in Asia after jumping more than one cent in New York as the European Central Bank and Bank of England kept their low benchmark interest rates unchanged.
The euro's strength also benefited from the ECB's assurances that it was ready to support crisis-hit countries.
ECB chief Mario Draghi said the bank's new bond-buying "bazooka" was primed and ready to help crisis-hit countries but stressed it was now up to governments to act and get their economies and finances in order.
Trade remained cautious, analysts said, as investors awaited US unemployment and jobs data for September, which was due later in the day.
The dollar was largely lower against other Asia-Pacific currencies, falling to 51.61 Indian rupees from 51.92 rupees on Thursday, to 41.40 Philippine pesos from 41.58 pesos and to 30.55 Thai baht from 30.67 baht.
It declined to Sg$1.2269 from Sg$1.2307, to 1,110.25 South Korea won from 1,113.35 won, to Tw$29.24 from Tw$29.28 and to 9,589 Indonesian rupiah from 9,598 rupiah. The Australian dollar rose to $1.0270 from $1.0210.
China's yuan changed hands at 12.43 yen, against 12.51 yen.