* Policymakers plan 2 trillion yuan rescue - Bloomberg News

* Shanghai Composite up 0.5%; Hang Seng surges 2.6%

* Yuan heads for best session this year

SHANGHAI, Jan 23 (Reuters) - Chinese stocks were lifted from multi-year lows on Tuesday by a news report and cabinet pledge flagging support for the country's battered equity markets, though the mood was fragile following a bruising start to 2024.

The Shanghai Composite hit a four-year low in morning trade, then closed 0.5% higher, while the blue-chip CSI300 closed up 0.4%. Hong Kong's Hang Seng closed up 2.6%, its largest one-day gain in two months.

All three indexes have performed poorly in January and have lagged world stocks for several years as investors have lost patience with the Chinese economy's underwhelming post-pandemic performance and a lack of big-ticket stimulus seen in past downturns.

China's CSI 300 Index is down 47% since it peaked in February 2021 and the HSI has sunk 49%.

China's cabinet said on Monday it will take forceful and effective measures to stabilise market confidence. Bloomberg News, citing unidentified sources, said policymakers were seeking to mobilise about 2 trillion yuan ($279 billion), mostly from offshore accounts of state enterprises, to fund equity buying through a China-Hong Kong stock exchange link.

Traders' response was warm but without much conviction.

The purported rescue package "is a welcome measure and shows increasing responsiveness ... but at under 2% of GDP, we fear this is still inadequate," said Aninda Mitra, head of Asia macro and investment strategy at BNY Mellon Investment Management.

"I would not be surprised by a short-term boost in sentiment and prices. But I doubt its sustainability unless these are complemented by a broader package of far-reaching reforms."

The China Securities Regulatory Commission did not respond to a Reuters request for comment, and analysts were also hesitant to cheer.

"We doubt if the size is accurate or the government is decisive enough to mobilise such a big amount for now," said Bank of America Securities analysts in a note to clients.

"In 2015-16 it took six months for the government to eventually stabilise the market. The market should not expect the move of the National Team to be effective immediately."

Traders noticed state banks supporting the yuan offshore - spiking yuan rates in Hong Kong - and driving it to 7.1630 onshore and toward its largest percentage gain of the year.

BATTERED BOUNCE

The best equity performances on Tuesday came from the most beaten-down sections of the markets and for exchange-traded funds tracking foreign stocks.

The Hang Seng index of mainland property companies rose 5.1%, after hitting a record low on Monday amid China's deepening housing crisis. The Hang Seng tech index, which hit a 15-month low on Monday, bounced 3.7%.

On the mainland, shares of securities brokers, firms developing artificial intelligence products and coal miners rose more than 2% each. Foreigners bought a net 3.8 billion yuan of China stocks on Tuesday.

Foreign exposure was popular domestically as global markets have made a steadier start to the year.

E Fund MSCI USA 50 Index ETF and the Fullgoal Nasdaq 100 ETF - both of which trade at hefty premiums to their net asset values - each surged by the 10% daily limit.

The ChinaAMC Nomura Nikkei 225 Index ETF (QDII) rose 4.9% as the Nikkei swept to new three-decade highs.

China anime comic gaming stocks climbed 5.8% after the regulator took down draft rules to control spending in video games from its website, checks by Reuters showed.

Structured derivatives nicknamed "snowball" products, which pay income provided the shares underlying them stay within a range, have also been a weight on markets as the major indexes fall to levels that trigger forced selling. The Shanghai Composite, for example, remains under the psychological 2,800 level.

Those who are hopeful of recovery point to evidence of state-fund buying reminiscent of 2015, such as recent soaring turnover in blue-chip ETFs.

Liang Zhu, chief investment officer at AllianceBernstein in China, said "what happened in China markets in recent days might be the 'last drop' investors could experience."

"As a long-only investor, we are very optimistic, it's almost the freezing point and the government will take action," he said.

Most investors, however, seem to be biding their time.

"The market is cautious toward anything that appears flimsy," said Simon Yu, vice general manager of Panyao Asset Management. "If there's nothing concrete, only vague rhetoric, investor expectations would remain pessimistic." ($1 = 7.1722 Chinese yuan)

(Reporting by Shanghai Newsroom; Editing by Sherry Jacob-Phillips and Kim Coghill)