Asian stocks and the euro steadied on Tuesday, but sentiment remained fragile on concerns that efforts to contain the euro zone debt crisis were faltering and tougher rules to strengthen banks' capital would further undermine their profits.

Sentiment in Asia was already risk-averse, after the death of North Korea leader Kim Jong-il raised fears of regional instability and prompted investors to pull money out of riskier assets and into the safe-haven dollar on Monday.

Market players said thin pre-holiday trade was likely to exaggerate price swings, but that further heavy selling was unlikely until there was another catalyst, such as European sovereign ratings cuts.

MSCI's broadest index of Asia Pacific shares outside Japan inched up 0.4 percent on Tuesday, after sliding as much as 2.9 percent the day before. South Korea's benchmark index <.KS11> led the gains with a 0.7 percent rise, after plunging as much as 5 percent on news of Kim's death on Monday. <.KS>

Tokyo's Nikkei share average <.N225> rose 0.65 percent, after hitting a new three-week low on Monday. <.T>

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Kim's death triggered immediate nervousness in the region, with South Korea stepping up its military alert, while Beijing, Pyongyang's neighbour and only powerful ally, affirmed its close ties. North Korea appears to have identified Kim's youngest son, Kim Jong-un, as his successor.

Developments overnight helped ease some risks of immediate disorder ... triggering a rebound across the markets, which were spooked and overshot yesterday, said Makoto Noji, senior strategist at SMBC Nikko Securities.

But it's nothing more than buying back in oversold markets, given very little positive news to recover confidence, he said.

EUROPE WOES CAP

European finance ministers failed on Monday to boost resources at the International Monetary Fund by a targeted 200 billion euros, agreeing to raise 150 billion euros, leaving doubts about whether the scheme would work with London, Washington and Germany's Bundesbank unenthusiastic.

With worries that the region's scheduled permanent bailout fund is insufficient to handle the debt problems, the increase in the IMF resources was seen as a vital part of Europe's steps to prevent the debt crisis from spinning out of control.

European policymakers made some progress in pursuing fiscal consolidation in Europe earlier in the month, but their failure to nail down a convincing commitment for the crucial bailout programme has prompted rating agencies to warn of downgrades for several euro zone countries, including France.

Credit ratings cuts of core European countries would further undermine the ability of highly-indebted euro zone countries to tap funds as they face soaring borrowing costs, and could derail progress towards resolving the euro zone's debt crisis.

Concerns about the European situation will keep the euro under pressure even if it manages short-term rises, said Sumino Kamei, a senior currency analyst at Bank of Tokyo-Mitsubishi UFJ.

European Central Bank President Mario Draghi warned of substantial downside risks to the economy and forecast 2012 as a difficult year for banks.

His comments weighed on the U.S. financial sector, sending the stock price of Bank of America , the largest U.S. bank, below $5 for the first time since March 2009.

Dollar funding strains intensified, with the costs for euro zone banks to borrow dollars rising. The benchmark London interbank offered rate on three-month dollars rose for a seventh straight session to 0.56695 percent on Monday, the highest level since July 2009.

The euro hovered around $1.3000 on Tuesday, little changed from late in New York and off Monday's low of around $1.2983. It hit an 11-month low of $1.2944 last week.

Commodities also steadied after coming under selling pressures on Monday. U.S. crude futures gained 0.5 percent on Tuesday, while gold edged 0.3 percent higher to $1,597.30, off Monday's lows near $1,582 an ounce.

Asian credit markets firmed as other markets stabilised, with spreads on the iTraxx Asia ex-Japan investment grade index narrowing by a couple of basis points on Tuesday.

(Additional reporting by Lisa Twaronite in Tokyo; Editing by Alex Richardson)