The early weakness was sparked by rising numbers of infections in major states including California, which reported a record 4,364 number of new infections on Saturday, Texas and Florida, and a number of other states including Arizona, Nevada, Missouri, South Carolina and Utah also reported record infections over the weekend.
This was reinforced by the news that Apple has again closed stores in states, including Arizona, Florida and North and South Carolina.
However, the US markets are also focusing on a number of states, including New York, that are starting to reopen after gaining control of infections and the likely boost to the US economy that will provide.
An estimated 300,000 New Yorkers will return to work this week.
The NZ market is also starting to look ahead to Wednesday when the Reserve Bank will announce its latest monetary policy decision.
Gilligan said he isn't expecting any fireworks from the RBNZ, pointing to an interview governor Adrian Orr gave CNN last week in which he said the central bank isn't taking anything for granted and that it is braced for the worst-case scenario of a move back to lockdown.
Orr said everyone around the globe faces the challenge of remaining on alert even when the virus was contained.
Reserve Bank of Australia governor Philip Lowe spoke on a webinar earlier today and noted that a lower Australian dollar would help that economy but that it isn't over-valued.
Lowe said a rising currency could become a problem at some point, "but I don't think we've reached that point yet."
Gilligan said both the Australian and NZ dollars have been rising as the US dollar weakened and that there's little either governor can do about that.
"You wouldn't stand in the way of the US dollar falling, but there's definitely a tightening of monetary policy going on in both countries," Gilligan said.
The kiwi has risen from below 55 US cents in mid-March.
The New Zealand dollar was trading at 93.59 Australian cents from 93.60 on Friday, at 51.88 British pence from 51.65 pence, at 57.39 euro cents from 57.24 cents, at 68.75 yen from 68.59 yen and 4.5507 Chinese yuan from 4.5491 yuan.
The bid price on the two-year swap was at 0.2150 per cent from 0.1850 per cent, while the 10-year swap was at 0.7025 per cent from 0.7225 per cent yesterday.