(Bloomberg) -- BlackRock Inc. closed-end fund holders are being urged by an influential proxy adviser to reject efforts by activist hedge fund Saba Capital Management to terminate the firm as manager of two funds overseeing about $2 billion.

Still, in reports released late Monday, Institutional Shareholder Services recommended supporting Saba’s board nominees for the two funds, noting concerns over their governance structures.

ISS urged shareholders to reject Saba’s proposals to terminate BlackRock as the investment adviser of the California Municipal Income Trust (BFZ) and BlackRock Science and Technology Term Trust (BSTZ), while recommending they support board nominees put forward by Saba for each fund, according to the reports seen by Bloomberg.

Saba “has presented a compelling case for change at the board level, but has not made a case for termination of the management contract at this time,” ISS said in the BFZ report.

BlackRock’s closed-end shareholders will vote next week on Saba’s proposal to nominate new board members at six closed-end funds and to remove the firm as manager of certain funds. On Tuesday, proxy adviser Glass Lewis weighed in on proposals for three of the six closed-end funds — backing all of BlackRock’s nominees and urging shareholders to retain the firm as manager.

Boaz Weinstein’s Saba has spent years and billions of dollars buying up closed-end funds trading at steep discounts and then pressuring managers to close the gap via tender offers and other means. BlackRock has pushed back against Saba’s claims that the firm is mismanaging its closed-end funds, telling investors that the hedge fund is attacking the funds “all to enrich itself.”

BlackRock praised Glass Lewis’s “broad support” in a statement Tuesday, while describing the ISS recommendation as a “vote of confidence” in a separate statement.

“As trusted fiduciaries, our commitment to all shareholders is unwavering, and we will continue to defend and advance their best interests,” R. Glenn Hubbard, chair of the boards of BlackRock closed-end funds, said in the statement.

Meanwhile, Saba said in a statement that ISS is holding BlackRock accountable for disregarding shareholder rights. “BlackRock’s hand-picked trustees are directly responsible for destroying billions in shareholder value and preventing us from taking action to protect our investment,” Saba partner and portfolio manager Paul Kazarian said in the statement.

The proxy recommendations are the latest development in an intense showdown between Saba and BlackRock, whose outcome could potentially shake up the $250 billion closed-end fund industry. 

Saba is pushing for boardroom changes at 10 BlackRock funds in total, contending its board candidates will improve the funds’ financial returns by closing the discount between the market price and their net asset value.

Last month, BlackRock released plans to waive some management fees and increase distributions at some closed-end funds, as Weinstein issued a fresh attack against the vehicles.

In its reports Monday, ISS had mixed recommendations for four other funds in which Saba is also looking to win board seats.

ISS supports BlackRock’s slate of directors for the New York Municipal Income Trust (BNY) and MuniYield Pennsylvania Quality Fund (MPA). For the MuniHoldings New York Quality Fund (MHN) and MuniYield New York Quality Fund (MYN), ISS supported one BlackRock nominee, but recommended that shareholders withhold support for another BlackRock director.

ISS has not yet published recommendations on four additional funds in which Saba is seeking to remove BlackRock as adviser. These include the BlackRock Capital Allocation Term Trust (ticker BCAT), BlackRock Innovation & Growth Trust (ticker BIGZ), BlackRock Health Sciences Term Trust (ticker BMEZ) and BlackRock ESG Capital Allocation Term Trust (ticker ECAT).

--With assistance from Crystal Tse.

(Updates with additional fund details in final paragraph.)

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