The Nikkei 225 index at the Tokyo Stock Exchange opened down 0.04 percent or 4.23 points at 9,549.77.
But dealers said a weakening yen was positive for Japanese firms.
"A weaker yen is stoking expectations for a V-shaped recovery in Japanese firms' earnings," Hiroichi Nishi, general manager of equity division at SMBC Nikko Securities, told Dow Jones Newswires.
The dollar stood at 80.27 yen, compared with 80.29 on Wednesday in New York, a day after breaking the 80-yen barrier for the first time in more than six months.
The euro was trading at $1.3255 and 106.43 yen, slightly higher than $1.3252 and 106.41.
The Dow Jones Industrial Average closed 27.02 points lower (0.21 percent) at 12,938.67.
International ratings agency Fitch said on Wednesday that a Greek default was "highly likely" as it cut its credit rating on Greece just a day after Athens agreed a massive debt bailout.
Fitch said it had cut Greece's long-term sovereign debt rating by two notches from "CCC" to "C", which meant it was now at the bottom of the speculative grades and just one step above formal default.» And eurozone private sector activity fell back in February after returning to growth in January, a survey showed, adding to concerns the region is flirting with recession.