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Jan 8 (Reuters) - Two British investment trusts run by Janus Henderson JHG.N have called on investors to reject a proposal by Saba Capital Management to replace their entire boards, a change they said would effectively cede control to the U.S. activist investor.

Saba Capital Management, run by prominent investor Boaz Weinstein, said last month it was trying to overhaul the boards of seven UK investment trusts over performances it described as ranging from "underwhelming" to "disastrous".

In a statement on Wednesday, Wendy Colquhoun, chairman of one of the two trusts, Henderson Opportunities Trust plc, said Saba's resolutions carried "significant uncertainty and risk".

The trust is currently offering shareholders the choice of a full cash exit at net asset value, or the option to roll over into an open-ended fund managed by Janus Henderson Investors.

"Saba is attempting to take control of the company with no assurances as to what will happen to shareholders' investments," she said.

"The board's message to shareholders is clear: please exercise your vote and don't let Saba take unnecessary risks with your money."

The European Smaller Companies Trust ESCT.L, another Janus Henderson-managed fund targeted by Saba, also called on Wednesday for shareholders to reject the proposal, with its Chairman James Williams in a statement calling Saba's motives "self-serving".

Saba did not immediately comment on Wednesday's releases by the two investment trusts.

The other trusts it is targeting include Baillie Gifford US Growth Trust USAB.L, CQS Natural Resources Growth & Income CYNL.L, Edinburgh Worldwide Investment Trust EWI.L, Herald Investment Trust HRI.L and Keystone Positive Change KPCK.L.

Keystone on Monday also hit back at the activist and said they were "appalled by Saba's actions and conduct".

In a statement supplied to Reuters in response, Saba said it had a successful track record in closed-end activism that has provided "liquidity, low fees and better management to deliver long-term value for all shareholders".

(Reporting by Yamini Kalia in Bengaluru; Editing by Mrigank Dhaniwala, Sinead Cruise and Jan Harvey)

((Yamini.Kalia@thomsonreuters.com;))