The dollar also weakened against the Japanese yen, with the dollar-yen pair trading as low 106.35 on Monday during Asian hours, compared with levels ranging from around 108-111 last week before the release of the U.S. jobs numbers.
As of 2:15 p.m. HK/SIN time on Monday, the dollar/yen erased some losses to trade at 106.95.
But the slight advance in the dollar/yen pair during the session did not fully ease the pressure on Japanese export stocks. Major exporters mostly finished lower, with Toyota shares falling 0.14 percent, Nissan down 1.25 percent and Honda off by 1.87 percent. But Sony shares erased early losses, ending up 0.42 percent.
A stronger yen is a negative for exporters as it reduces their overseas profits when converted into local currency. On Wednesday Japan's Prime Minister Shinzo Abe announced a delay in the country's planned sales tax hike and detailed a new stimulus package to revive the Japanese economy. That move also had spurred the yen higher.
Helping to bolster the Nikkei index, shares of Softbank, which has an around 4 percent weighting in the benchmark index, ended up 1.21 percent after the Japanese internet and telecom giant said it will sell most of its stake in GungHo Online Entertainment in a deal valued at 73 billion yen.
That follows Softbank's announcement last month that it would sell at least $7.9 billion worth of its stake in Chinese internet giant Alibaba to raise capital.
The Australian dollar advanced on Friday, moving from as little as $0.7214 before the jobs report on Friday to levels as high as $0.7391 on Monday before retreating to around $0.7330 as of 2:28 p.m. HK/SIN.
Also providing some support to the Aussie, on Tuesday, data showed Australia's first quarter gross domestic product grew 1.1 percent in the three months to March. Analysts suggested the Reserve Bank of Australia (RBA) would likely leave monetary policy unchanged at its next meeting. In its May meeting, the RBA lowered the cash rate by 25 basis points to a record low 1.75 percent.
"However, the minutes from the last RBA meeting indicated that the decision was a close one, so the tone of the RBA statement could be slightly less dovish," said Kathy Lien, managing director of foreign exchange strategy at BK Asset Management, in a Friday note.