The trade-weighted index declined to 71.94 from 72.19 on Thursday, and is heading for a 0.2 per cent increase on the week.
A survey of 13 currency analysts on Monday predicted the kiwi would trade between US68c and US71.20c this week.
A meeting of euro-zone finance ministers broke up without agreement on Greece and talks are set to resume today.
German Chancellor Angela Merkel warned that Germany would not be "blackmailed" and in a closed-door meeting with her party members in Berlin stressed a deal had to be done before financial markets opened next week.
"All eyes are on the weekend because we're going to have the Greek saga over the weekend and I still think there's a fair chance it gets kicked through to Tuesday," said Tim Kelleher, head of institutional FX sales NZ at ASB Institutional in Auckland
If a deal could not be reached, that would sap investors' appetite for riskier assets such as equities, "and that feeds into a lower kiwi".
Kelleher said liquidity would probably be thin on Monday, meaning moves in the kiwi dollar could be exaggerated if Greece and its lenders can't strike a deal.
The kiwi was little changed at 61.55 euro cents as at 5pm yesterday from US61.69c on Thursday, and is heading for a 1.2 per cent weekly gain.
The kiwi traded at A89.16c from A89.27c on Thursday, and fell to 4.2757 Chinese yuan from 4.2932 yuan. It dropped to 84.96 from 85.48 on Thursday, and fell to 43.74 British pence from 44.05p.