In midday Tokyo trade, the greenback rose to 103.19 yen from 102.91 in New York.
The euro weakened to $1.3305 from $1.3321, while it strengthened to 137.28 yen against 137.07 yen in US trade.
Traders moved out of the yen -- seen as a safe-haven currency in times of turmoil -- after the upbeat US data and as investor concerns about a clash between Russia and Ukraine eased.
Housing starts in the world's biggest economy jumped 15.7 percent in July to their strongest level since last November, while new building permits rose 8.1 percent.
Easing geopolitical jitters, Russian President Vladimir Putin and his Ukrainian counterpart will meet next week for the first time in two months. The gathering will also involve senior European Union officials.
The dollar rally also came ahead of Wednesday's release of minutes from the policy-setting Federal Open Market Committee's last meeting.
Analysts will pore over the minutes for signs of whether the Fed might accelerate the timeline for raising interest rates, now expected in the second half of 2015.
"At the July 29-30 FOMC Meeting, the (Fed) was relatively dovish on the labour market, but acknowledged that the inflation risks had risen," National Australia Bank said in a note.
"So the minutes will again highlight the debate between the hawks and the doves," it added.
The dollar's upside against the yen was limited ahead of Federal Reserve chair Janet Yellen's keynote address at the central bank's annual economic conference this week.
The yen's losses may have also been driven by lacklustre Japanese trade data published Wednesday.
The report came a week after second-quarter economic growth suffered its biggest contraction in about three years after a sales tax hike in April dented growth.
"With a number of Japanese economic indicators having deteriorated markedly in the past two months, economists have become more cautious in their Japan outlook," Credit Agricole said.
"So too have investors seeing the probability they attach to additional BoJ easing rise steadily in recent weeks."
Further easing measures from the central bank would tend to weaken the yen.