The antipodeans bounced from near 16-month lows against the Japanese yen and were well bid on the US dollar as well.
The Australian dollar rose 0.6 percent to 81.07 yen after going as deep as 80.51 on Friday, the lowest since November 2016. In the two weeks ended Friday, the Aussie lost about 4 percent against the Japanese currency.
The New Zealand dollar also nudged higher to 76.28 yen from a recent trough of 75.54. The cross fell about 1 percent last week.
Global markets were shaken after US President Donald Trump moved to impose tariffs on Chinese goods, edging the world's two largest economies closer to a trade war. The tariffs were on top of import duties on steel and aluminium levied on a number of countries, including China.
The Asian giant has promised, in no ambiguous terms, that it would retaliate.
"Traders are continuing to look to safe haven products with the Japanese yen, in particular, having a very strong finish to the week both against the dollar and on the crosses," said Nick Twidale, chief operating officer at Rakuten Securities Australia.
Twidale noted positive headlines over the weekend toward resolving the trade spat, with China and the United States holding dialogues to reach an agreement.
The United States also agreed to exempt South Korea from steel tariffs, instead imposing a quota on steel imports as the two countries renegotiate a trade deal.
"If we do start to hear more favourable news from the US administration and indeed from the Chinese side over the next few trading sessions, then we may see a sharp reversal of the recent moves in the market," Twidale added.
Against the greenback, the Aussie was up 0.4 percent at $0.7727 from last week's trough of $0.76720. The kiwi bounced 0.6 percent to $0.7270, the highest since March 16.
New Zealand government bonds rose, sending yields about 3.5 basis points lower at the long end of the curve.
Australian government bond futures were mixed, with the three-year bond contract up half a tick at 97.845. The 10-year contract eased half a tick to 97.3350.