The proposed package, worth as much as 86 billion euros is expected to meet Greek financing needs for the next three years in return for changes to Greece's tax and pension systems, further privatisation of assets, and market reforms.
Optimism about stability in Greece turned investor attention to US interest rate hikes, which supported the greenback.
"Following marathon negotiations, Greece and its creditors reached an arrangement this morning that provides the basis for a third bailout package," ANZ Bank New Zealand senior economist Mark Smith and senior FX strategist Sam Tuck said in a note.
"As long as this deal holds, a potential roadblock to Fed policy normalisation has been removed, with lift-off from later this year still on track."
ANZ expects the kiwi to trade between 66.30 US cents and 67.60 cents today.
Today, the focus will be on the Australian NAB business confidence report, while tonight traders will be eyeing US retail sales data and inflation readings from the UK and Germany.
Traders will continue to watch developments in Greece as the Greek parliament needs by Wednesday to legislate at least four of the key agreed reforms and endorse the remaining measures.
The New Zealand dollar slipped to 90.31 Australian cents from 90.42 cents yesterday, advanced to 60.84 euro cents from 60.45 cents, fell to 43.20 British pence from 43.43 pence and edged up to 82.60 yen from 82.51 yen.