The Australian dollar was a shade weaker at $0.6907, extending losses for the seventh straight day. It hit a day's trough of $0.6900, a level not seen since June 20.
The Aussie ended last week down 1.9% to cap its worst weekly performance since early February.
The New Zealand dollar slipped 0.1% to $0.6627, a level not visited since July 10. It lost 1.9% last week after notching two straight weekly gains.
Market attention is squarely on a rate decision by the U.S. Federal Reserve on Thursday. Markets are fully priced for a 25-basis-point reduction, and the key issue for traders will be on the outlook given expectations are centred on several more cuts over the next year.
The U.S. employment report on Friday will provide further clues about the health of the world's biggest economy and likely help gauge the Fed's future policy track .
At home, data out on Wednesday will likely show the consumer price index (CPI) up a touch to 1.5% in the second quarter but still below the Reserve Bank of Australia's (RBA) medium-term target of 2% to 3%.
"Any miss on the headline would likely increase market pricing for an August cut, currently around 20% priced," National Australia Bank analyst Tapas Strickland said in a note.
The RBA has already chopped interest rates twice to an all-time low of 1% and financial markets are predicting a third cut before Christmas this year.
The Reserve Bank of New Zealand (RBNZ) is expected to cut its rates to 1.25% in August, and to 1% by February next year .
RBA Governor Philip Lowe last week underlined the bank's easing bias by saying rates were expected to be low for an "extended period."
Such expectations, together with a stronger greenback , are putting a lid on the Aussie and kiwi, and sending bond yields to record lows.
Yields on two-year New Zealand paper were at historic lows of 1.065% while those on Aussie 10-year bonds were down at 1.192%, having fallen a hefty 12 basis points last week. The three-year Aussie bond future hit a record peak of 99.225.
"The AUD remains on the backfoot," Strickland said. "It is a very busy week ahead with Wednesday shaping up to be a key focal point with a likely U.S. rate cut and Aussie Q2 CPI."
"The messaging in the post-meeting statement and the press conference will be key and will help markets determine whether the rate cut is just an 'insurance cut', or Fed is embarking on a full easing cycle as the market currently prices in."