Halliburton Co., the giant oil-field services company once headed by Vice President Cheney, said yesterday that it has reached an agreement valued at roughly $4 billion that would settle "all present and future asbestos claims, fully and permanently resolving all personal injury asbestos liability."

The agreement, which must be approved by a federal bankruptcy court in Pittsburgh, calls for the company to put up as much as $2.775 billion in cash, along with 59.5 million Halliburton shares and $100 million in notes.

These assets would go into a pool to pay present and future claims of individuals injured by asbestos.

The settlement was reached with attorneys representing substantially more than the 75 percent of present asbestos claimants required for resolution on all of the cases, the company said. But it noted that the deal remains contingent on Halliburton's ability to borrow enough to meet its commitments.

"If this transaction is completed, it will resolve a major issue that has been clouding our future," Halliburton chairman and chief executive David J. Lesar said in a statement yesterday.

"While I am pleased with the progress on the settlement we have made," he added, "I must caution that there is much work to be done."

Several lawyers involved in the case said they view the settlement as a good one for current plaintiffs and for Halliburton. But one said he expected attorneys for some asbestos victims, including some who have not yet filed claims, may conclude that their potential recoveries would be reduced and file objections to the plan.

Politics as well as economics played a role in pushing the parties toward settlement, according to some attorneys. The Republican victory in the November elections has increased the chances that some sort of national tort reform might be enacted, perhaps limiting damage recoveries. At the same time, those favoring such reform would like to see the Halliburton case resolved so that they could not be charged with acting to bail out the vice president.

The deal would be carried out through a "prepackaged" bankruptcy filing by Halliburton subsidiaries DII Industries (formerly Dresser Industries Inc.) and Kellogg Brown & Root Inc., plus some of their own subsidiaries. Halliburton itself would avoid bankruptcy, while continuing to own DII, KBR and other subsidiaries.

Halliburton bought Dresser in 1998 when Cheney was chief executive.

Bankruptcy Judge Judith K. Fitzgerald, who is already overseeing the reorganization of Harbison-Walker Refractories Inc., a company once owned by Dresser, scheduled a hearing on the settlement for Jan. 17 and continued a freeze on asbestos lawsuits against Halliburton.

Under the deal, DII and KBR would retain the rights to the first $2.3 billion of any insurance proceeds. According to company filings, Halliburton has insurance valued at as much as $4.1 billion. The amount of any ultimate payouts remains uncertain, however. Insurers are resisting Halliburton's claims and the sides are fighting in court in Texas and Pennsylvania over the issue.

Asbestos, a silicate mineral fiber, was widely used for many years in fireproofing, construction materials, automobile brakes and other products where heat resistance was important. The material performed very well in those applications, but the tiny fibers can cause severe lung damage and cancer when inhaled.

Over the years thousands of American workers and others were exposed to asbestos. Their claims have spawned thousands of lawsuits and driven dozens of companies into bankruptcy. The claims have been described as an "anchor" weighing down U.S. manufacturing and slowing the entire economy.

Large cases, such as Halliburton's, are increasingly resolved by establishment of a trust, funded by cash and stock from the company. The first and largest of these is the Manville Trust, which was set up in 1988 to pay claims against the former Johns-Manville Corp. As of Nov. 30, that trust has paid over $3 billion to nearly 500,000 claimants and other beneficiaries.