The two said on Friday that they had entered into an "information sharing and engagement agreement," which will allow for a "deeper level of engagement and cooperation."

The San Francisco-based hedge fund, one of the industry's most closely watched activist investors, unveiled a $1.2 billion stake in New York-based Citi last May, and said it liked the bank's low risk and reliable revenue.

ValueAct has increased its position in recent months and currently owns about 32 million Citigroup shares, or 1.3 percent of the outstanding, according to company filings.

The fund is one of the larger shareholders of Citigroup, the third-biggest U.S. bank by assets.

ValueAct, which differentiates itself from many more voluble activists, did not ask for a board seat at the time of its investment and said on Friday that it is not looking for one now. The agreement, which essentially offers the hedge fund rights that come with having a board seat, is a first for ValueAct, a firm known for working collaboratively and behind the scenes with target companies.

But when the time is right and some potential conflicts are eliminated, ValueAct is expected to propose a candidate for the board, the statement said. ValueAct currently holds a board seat at Alliance Data Systems Corp, which competes with Citigroup in issuing credit cards for retailers.

ValueAct generally holds core investments like Citigroup for three to five years, a person familiar with the fund said.

ValueAct and Citigroup on Friday declined to comment beyond the release.

By entering this agreement, the hedge fund is signaling its plans to likely become more involved with this bank than with Morgan Stanley, another name in its portfolio. ValueAct has invested roughly 35 percent of its portfolio in financial service companies.

Credit Suisse analyst Susan Roth Katzke called the agreement positive for Citi, saying the company faces "a stretch" to reach its return on tangible common equity target of 13 percent by 2020.

Citigroup has made a number of changes since ValueAct first commented on its stake in May in a letter to its investors. It parted ways with the head of its struggling branded-credit cards division, announced a reorganization of part of its investment bank, and named a new chairman and a new chief financial officer to replace those retiring.

Its shares have lagged those of other big banks because of doubts about its ability to increase revenue following extensive restructuring after the financial crisis.

Citigroup, which will report fourth-quarter results on Monday, was trading at $57.06 on Friday, up roughly 1 percent and outperforming the sector.

(Reporting by Svea Herbst-Bayliss and David Henry in New York, Editing by Jonathan Oatis and Rosalba O'Brien)

By Svea Herbst-Bayliss and David Henry