WASHINGTON – Citigroup Inc. said Friday it reached a deal that will give the government up to a 36 percent stake in the struggling bank.

The government, along with other private investors, will convert some of their preferred stock in Citi to common shares.

Citi will offer to exchange up to $27.5 billion of its existing preferred stock held by private investors at a conversion price of $3.25 per share, a 32 percent premium over Thursday’s closing price of $2.46. The government will match up to $25 billion of preferred stock it currently owns for conversion at the same price.

If the maximum amount of preferred stock is converted, current common stockholders will see their ownership stake fall to about 26 percent.

The conversion will help provide Citi the mix of capital to withstand further weakening in the economy.

The Government off Singapore Investment Corp., Saudi Arabian Prince Alwaleed Bin Talal, Capital Research Global Investors, Capital World Investors are among the private investors that said they would participate in the exchange.

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