The Nikkei was 0.51% higher.
Australia's S&P/ASX 200 has climbed 0.75%.
U.S. futures were also pointing up.
Japan's trade deficit unexpectedly increased, new data showed, with export growth slowing sharply to 11.5%, versus expectations for 16.1%.
This is expected to be a busy week, as the backlog of government data begins to ease. Most prominently, we're going to get the delayed non-farm payrolls reading Tuesday.