SYDNEY, Sept 15 (Reuters) - The Australian dollar came under pressure on Tuesday as odds narrowed for further monetary policy easing by the country's central bank while its New Zealand peer held steady.

The Aussie was last a shade weaker at $0.7285. The currency has meandered since hitting a two-year high of $0.7413 on Sept.1 as market pricing shifted rapidly for a cut to the cash rate to 0.1%.

Interest rate futures are almost fully pricing in a 15 basis point rate cut at the Reserve Bank of Australia's (RBA) Oct. 6 policy meeting.

The RBA last cut the cash rate to an all-time low of 0.25% in an emergency meeting in March and has repeatedly said the benefits of taking rates deeper into record territory were limited.

But at its September board meeting, Governor Philip Lowe hinted at additional policy measures to support an economy reeling from its worst contraction in almost a century.

The remark stoked speculation of further easing.

The market is now awaiting minutes of the RBA's Sept.1 policy meeting due out at 0130 GMT for clues about its future course of action.

"The RBA Minutes...may show discussion on any further tweaks to policy the RBA is considering," NAB senior forex strategist Rodrigo Catril wrote in a note.

Catril referred to a news story in the Australian Financial Review on the weekend saying the RBA was contemplating further policy easing, including an expanded bond buying program and possibly lowering the cash rate.

"This saw selling pressure on the AUD and gains in the NZD, suggesting closing of long AUD/NZD positions might have been a factor," Catril said.

Against the New Zealand dollar, the Aussie slipped to a one-week low overnight to $1.0854. It pared some of the losses to be last at $1.0871.

The New Zealand dollar was fetching $0.6699, above a recent trough of $0.6602, partly on news the country would lift coronavirus restrictions across the country on Sept. 21.

"NZD’s outperformance can probably be partly attributed to news that the NZ Government is looking at easing virus restrictions, although we suspect the AUD/NZD underperformance played a bigger role on the flying kiwi amid selling pressures on the cross," Catril said.

New Zealand government bonds were slightly weaker with yields up about 1 basis point at the long end of the curve.

Australian government bond futures were little changed, with the three-year bond contract at 99.734 and the 10-year contract at 99.116. (Editing by Shri Navaratnam)