* RHB announced $565 million rights issue in April

* But Aabar unhappy with sliding value of its stake

* Malaysia currency, markets hit by worsening trade position

* Malaysian PM under pressure from 1MDB controversy

* Impetus for Abu Dhabi-Malaysia ties may have shifted

By Yantoultra Ngui and Stanley Carvalho

KUALA LUMPUR/ABU DHABI, Sept 28 (Reuters) - Abu Dhabi state fund Aabar Investments may refuse to invest in a 2.5 billion ringgit ($565 million) rights issue by RHB Capital in a sign of disappointment among Gulf investors with economic and political instability in Malaysia.

RHB, Malaysia's fourth largest bank by assets, announced the rights issue in April to support its growth and meet regulatory requirements for capital. Aabar owns about 21 percent of the bank.

But three sources with knowledge of the matter told Reuters in the last few days that Aabar was unlikely to buy into the offer, at least partly because it was disappointed by the performance of its investment in RHB as Malaysia's currency and financial markets sag.

"Aabar isn't too happy with their investment in RHB and they aren't going to subscribe," said a Malaysian investment banker who is in contact with RHB, declining to be named because of commercial sensitivities.

Spokesmen for Aabar and RHB declined to comment.

Malaysia's markets have been hit this year by a worsening of its trade position due to weak prices for liquefied natural gas exports, and by allegations of mismanagement and graft at state fund 1Malaysia Development Bhd (1MDB), whose advisory board is chaired by Prime Minister Najib Razak.

Shares in RHB are down 21 percent since the end of 2014 and 44 percent lower than the price at which Aabar bought its RHB stake from Abu Dhabi Commercial Bank ADCB.AD in June 2011. The stake is now worth about $740 million.

RHB said last week that it was extending the period for subscriptions to its rights issue by nearly two months, after Malaysia's central bank ordered that Aabar be allowed to buy no more than 15 percent of the rights - a restriction included in the 2011 deal through which Aabar purchased its original stake.

The closing of the offer was delayed to Nov. 23 "to allow time for the board to engage with the relevant regulators and to deliberate and implement the rights issue in the most efficient manner, after considering the order", RHB said last week.

But the sources told Reuters that regardless of the 15 percent restriction, Aabar was reluctant to buy any rights.

A second investment banker in Malaysia said he had been told by Aabar executives that the Abu Dhabi fund was not subscribing at all. There was hardly any communication between Aabar and RHB, the banker said.

A source close to the senior management of Abu Dhabi's state-owned International Petroleum Investment Co (IPIC), the parent of Aabar, said Aabar was unlikely to subscribe.

He also said any investment by Aabar was unlikely for the forseeable future until management changes there were completed. Aabar appointed a new chief executive, Mohamed al-Mehairi, last month; its chairman stepped down earlier this year.

Abu Dhabi and Malaysia have close investment and diplomatic ties, which strengthened after the 2008-09 global financial crisis. The relationship allowed Abu Dhabi to deploy some of its vast oil wealth in Malaysia, a moderate Muslim-majority nation with a fast-growing economy.

The impetus for the relationship may have changed at least temporarily, however, as the Malaysian economy has run into headwinds and low oil prices have slashed the financial surplus which Abu Dhabi has available to invest abroad.

In May, IPIC effectively agreed to bail out loss-making 1MDB, undertaking to provide it with $1 billion in cash, assume $3.5 billion of 1MDB debt and forgive an undisclosed amount of debt owed to IPIC by 1MDB.

In exchange, IPIC was to receive assets from 1MDB. But these assets have still not been publicly named, and their value may have declined in recent months as the Malaysian ringgit has tumbled and the controversy over 1MDB's operations has increased, putting pressure on Najib's government.

(Writing by Andrew Torchia; Editing by mark Heinrich) ((andrew.torchia@thomsonreuters.com; +9715 6681 7277; Reuters Messaging: andrew.torchia.thomsonreuters.com@reuters.net))