That killing, on top of other recent killings of black people, has sparked protests throughout the US as well as globally. In some places the protests have turned violent, with buildings destroyed and shops looted. Trump has called the protesters "thugs."
Stephen Innes, chief global markets strategist at AxiCorp, said that "putting boots on the ground to quell civil unrest never ends well.
"Anarchy in the streets threatens to throw a wet blanket on risk recovery as investor optimism over the economic reopening in the US could wane," Innes said.
"If American consumers were reluctant to come out of their covid-19 lockdown cocoon, fearing a secondary spread, it's unlikely they will feel any safer with military Humvees rolling down Pennsylvania Avenue," he said, referring to the street the White House is on.
Mike Shirley, a dealer at Kiwibank, said the kiwi dollar had benefited from a "general risk-on environment" which was generated by "that China recovery - them and the world opening up again and people feeling just a little bit better about the covid thing."
The Reserve Bank of Australia's latest monetary policy statement, in which it said it would maintain current policy settings, had no impact on currency markets.
Shirley said the next set piece the market is looking to will be the US non-farm payrolls data due on Friday.
Currently, the market is expecting the loss of a further eight million jobs, following last month's 20.5 million loss. The headline unemployment rate in the US is expected to rise to 19.5 per cent from 14.7 per cent a month ago.
The New Zealand dollar was trading at 92.45 Australian cents from 93.34 on Friday. It was at 50.31 British pence from 50.28 pence, at 56.43 euro cents from 55.90 cents, at 67.63 yen from 66.49 yen, and at 4.4716 Chinese yuan from 4.4380 yuan.
The bid price on the two-year swap rate was 0.1725 per cent from 0.2125 per cent on Friday, while 10-year swaps were at 0.7325 per cent from 0.7175 per cent.