The Aussie dollar was hanging on at $0.7173 after touching a six-week trough at $0.7151 on Friday. The kiwi dollar huddled near a three-week low of $0.6788, having shed 0.9 percent on Friday.
Both had been sideswiped by disappointing Chinese economic data, which in turn rippled through markets globally sending stocks sharply lower.
There was better news for Australia's bond market after the government more than halved its budget deficit forecast for 2018/19 and projected growing surpluses for following years.
A combination of lower benefit payments and stronger revenues from company profits and income tax has allowed the government to scale back its borrowing needs.
If everything goes to plan, Australia's net debt would shrink to just 1.5 percent of gross domestic product (GDP) by 2028/29, from this year's 18.2 percent.
Su-Lin Ong, head of Australian economics at RBC Capital Markets, said the improvement meant the government would be able to sell less paper at a time when US deficits were heading toward $1 trillion a year.
"Confirmation that the peak in issuance is well behind us with smaller funding tasks ahead is in marked contrast to the US fiscal dynamics and, in part, underpins our long Australian/short Treasury trade," she said.
Bonds have already been in demand as global growth cooled and investors scaled back expectations for how far and fast US interest rates might rise.
Yields on Australian 10-year paper last week dropped to their lowest since mid-2017 at 2.410 percent, having fallen 40 basis points in just a month.
Bond futures extended their gains on Monday, with the three-year bond contract up 1.5 ticks at 98.065. The 10-year contract firmed 2.25 ticks to 97.5550.
The kiwi dollar was still smarting from news the Reserve Bank of New Zealand's (RBNZ) was considering almost doubling the capital banks would need to hold to bolster financial system stability.
Jarrod Kerr, chief economist at Kiwibank, said the tightened rules could lead to slower credit growth and higher borrowing costs for banks and customers.
"Bank owners are being asked to stump up with a truck load more capital as a buffer against adverse shocks," he said.
"Our system will be that much safer in five years, but at the expense of growth near term. Credit is the oil in the economic engine, and the oil is now that much more expensive and in stricter supply."