United Rentals last week waived a condition to its ongoing tender offer that its stock cannot fall more than 10 percent below the June 16 closing price. United said the condition was triggered when the company’s shares dropped below $19.82, closing Monday at $19.61.

The Greenwich, Conn.-based company began its modified “Dutch auction” tender offer to buy back shares June 17. United Rentals is offering to buy up to 27.2 million common shares, representing about 31.4 percent of its outstanding stock, for $22 to $25 each. The tender offer is scheduled to expire July 16, unless extended by the company. United’s shares rose later in the day to $19.93.

United Rentals added that its executive officers and directors do not intend to participate in the offer. The company’s shares were priced at $18.95 at the close of trading Thursday.

United Rentals is No. 1 on the RER 100.