"Optimism around a Greek deal that had built up into week's end has faded somewhat this morning, as euro-zone leaders are yet to formally agree on a path forward," Bank of New Zealand currency strategist Raiko Shareef said in a note.
"We will soon see whether Greece elects to swallow this particularly bitter pill, as a signal of good will. That would open the path to detailed negotiations about (necessary) debt reduction.
"There remains some uncertainty about whether Germany and the other hard-line creditors will accept the proposal put up by the finance ministers.
"That has contributed to the slightly risk-off start to the week. We expect the New Zealand dollar to remain sensitive to risk appetite, but continue to see potential for a strong squeeze higher in the event of a deal being struck."
In New Zealand today, June data on food prices and house sales are expected to be released.
Traders will also be eyeing Chinese trade data for June, also scheduled for release today.
The New Zealand dollar slipped to 60.33 euro cents from 60.92 cents on Friday, fell to 43.17 British pence from 43.89 pence, dropped to 81.91 yen from 82.31 yen and edged lower to 90.29 Australian cents from 90.34 cents.