The casino and hotel operator Golden Nugget Inc. yesterday offered to buy 27 percent of the famed Hilton Hotels Corp. -- the first step in a proposed takeover that could be worth $1.8 billion.

Las Vegas-based Golden Nugget said it wanted to purchase the 6.8 million shares of Hilton held by trusts for the estate of Hilton founder Conrad N. Hilton. Golden Nugget said it would pay $72 a share for that stock, and if successful, would extend a similar offer to other Hilton shareholders.

But Barron Hilton, chairman of the company, said in a statement from Hilton's Beverly Hills headquarters that Golden Nugget's offer was "inadequate." He did not elaborate.

Hilton recently exercised an option to buy the estate's stock himself. It would be extremely difficult for Golden Nugget to proceed with its offer without Barron Hilton's approval, because in addition to serving as chief executive of the company, he also is co-trustee of the Hilton estate's holdings. Officials of both companies said they knew of no negotiations that may have already taken place between Hilton and Golden Nugget.

Hilton's stock soared yesterday to $72.12 a share, an $8.25 increase.

Golden Nugget is about half the size of Hilton. Its primary operations are hotel-casinos in Las Vegas and Atlantic City. Hilton owns or franchises dozens of hotels throughout the United States; Hilton hotels overseas are owned by another, unrelated company.

Both Hilton and Golden Nugget recently suffered setbacks in their efforts to expand operations in Atlantic City. Hilton has been unable to get a gambling license for its nearly completed $308 million hotel-casino in the New Jersey resort because state officials object to the company's ties to Chicago labor lawyer Sidney Korshak, who allegedly has links to organized crime. Golden Nugget, meanwhile, recently abandoned plans to build its own $300 million hotel-casino in Atlantic City, taking a $15 million loss on the project.

In a letter to Barron Hilton outlining the offer, Golden Nugget Chairman Stephen A. Wynn wrote, "As the owner of the Golden Nugget casino-hotels in Las Vegas and Atlantic City, we have extensive experience in both the gaming and hotel industries. We believe the acquisition of a significant interest in Hilton would be beneficial to Hilton and its stockholders, particularly in light of the recent developments in New Jersey."

Wynn also argued that the proposed transaction would provide for a "dramatic increase" in the income of the Conrad N. Hilton Foundation, which holds virtually all of the Hilton estate's stock. He estimated that the foundation could earn $60 million a year by reinvesting the proceeds of the proposed stock purchase, a fivefold increase over the foundation's current dividend income from its Hilton stock. Officials of the foundation could not be reached for comment.

Saying that "time is of the essence," Wynn said Hilton had until April 12 to make a decision on the offer, although he indicated that date could be extended if a probate court had to approve transfer of the Hilton estate's shares. If Hilton does not meet the deadline, Wynn said, the offer will expire.

Hilton had its origins in the Mobley Hotel in Cisco, Tex., which Conrad Hilton bought in 1919. Over the next six decades, Conrad Hilton built an impressive roster of hotels in many of the nation's major cities. Last year, the company earned $114 million on revenue of $686.6 million. Golden Nugget earned $5.2 million last year on revenue of $251 million.