* Yen broadly firmer, euro/dollar more subdued

* Asian stocks mostly lower, Japan shut for holiday

* Sterling briefly unsettled by domestic politics

By Ian Chua

SYDNEY, March 21 (Reuters) - The safe-haven yen was broadly firmer on Monday, particularly against its New Zealand and Australian peers, as the mood turned sour with most Asian share markets down.

The U.S. dollar and euro both eased 0.2 percent, to 111.35 yen and 125.59 yen respectively.

The kiwi shed 0.6 percent to 75.34 yen and the Aussie lost 0.4 percent to 84.43 yen.

Traders said a further dip in crude oil prices, which turned around from 2016 peaks on Friday, cast a shadow on risk appetites.

"It is an extension of a slightly cooler mood overall," said Sean Callow, senior currency strategist at Westpac Bank.

The euro was little changed against the U.S. dollar at $1.1276 as investors waited for European markets to open.

A public holiday in Japan and an absence of fresh drivers meant there was no conviction to push the market either way.

Sterling was a notable underperformer after British Prime Minister David Cameron was forced into a hasty cabinet reshuffle on Saturday following the shock resignation of a senior minister.

The pound was marked as far down as $1.4430, but has since returned to $1.4447, or 0.2 percent lower on the day.

All that left the dollar index little changed at 95.062, not far from a five-month trough of 94.578 set on Friday.

Dollar bulls were hit hard after the Fed last week held interest rates steady and cut in half the number of projected quarter-point hikes to just two this year.

Fed Chair Janet Yellen also sounded doubtful that a recent firming in U.S. inflation would be sustained, suggesting the central bank is in no hurry to tighten policy.

Euro bulls were not spared either. European Central Bank (ECB) chief economist Peter Praet on Friday said rates have not reached their lower limit yet.

His comments came a week after ECB President Mario Draghi upset the market by saying he did not expect further rate cuts were needed after unveiling a fresh set of stimulus. That saw the euro rebound from a low around $1.0821.

(Editing by Richard Borsuk)