SYDNEY, Feb 27 (Reuters) - The Australian and New Zealand dollars nursed heavy losses on Monday after breaching key support levels, as strong U.S. spending and inflation data stoked worries that the Federal Reserve would have to do more to contain runaway inflation.

The Aussie was hovering at $0.6732, having plunged 1.2% on Friday as far as $0.6719, the lowest since Jan. 4. It also breached its 200-day moving average of 68 cents, a key support level it had bounced off several times in the past week.

Now it has support at January's low of $0.6689 and December's $0.6629.

The kiwi dollar was reeling at $0.6165, after tumbling 1.0% the previous day to as low as $0.6153, the weakest since late November. It also snapped major support at $0.6182, which has turned into a near-term resistance level.

On Friday, data showed that U.S. consumer spending, which accounts for two-thirds of the economy's activity, rose by 1.8% in January, the largest increase in nearly two years.

Furthermore, the personal consumption expenditures (PCE) price index, the Fed's preferred inflation measure, accelerated by 0.6% last month, the biggest increase in six months and beating expectations.

That added to a recent strong run of U.S. economic data that has pointed to the strength in the world's largest economy, reinforcing bets that the Federal Reserve would have to do more to bring inflation down.

Indeed, Fed funds futures have now priced in a peak of 5.4% in September and expect it to stay above 5% for the year, compared with the current target rate of 4.5%-4.75%.

Investors are still leaning towards a quarter-point hike in March, but there is an increased risk that the Fed could pivot back to a 50-basis point hike in March.

"USD is likely to consolidate this week after last week's increase. However, the risk is for further gains in the USD early in the week following the strong PCE deflator, " said Joseph Capurso, head of international economics at CBA.

"AUD/USD will likely weaken further in the early part of the week though may carve out a bottom later this week."

The possibility of higher rates in the United States led investors to push up bets for local terminal rates.

The cash rate in New Zealand is now seen peaking at 5.5% later this year, compared with 5.2% just a week ago. New Zealand two-year swap rates jumped 5 basis points (bps) to 5.42%, the second highest level since 2008.

Australia's cash rate is now expected to peak at 4.4%.

The yield on three-year Australia government bonds rose 6 bps to 3.638% on Monday, while ten-year bond yields also increased 5 bps to 3.895%. (Reporting by Stella Qiu; Editing by Sonali Paul)