NEW YORK (AP) _ A restructured Manville trust is seeking friendlier relations with lawyers representing tens of thousands of workers made ill inhaling asbestos.

The trust's new chairman, Robert A. Falise, and other officials plan to meet with plaintiffs' lawyers in nine cities starting next month in an effort to avoid the acrimony and litigation that undermined the trust in the past.

But Falise, a former corporate lawyer, said Tuesday he will stress that victims awaiting money from the main mechanism for compensating asbestos- related illnesses should lower expectations for big payouts.

''That could create a lot of heat and fire. But I'd rather it came to the surface now ... so it doesn't slow down the process of getting this badly needed money to plaintiffs,'' he said.

The trust was created in 1988 in the bankruptcy case of Manville Corp., which was the nation's leading maker of products containing asbestos, the heat-resistant mineral linked to cancer and other serious lung ailments.

As of last Friday, the trust had received 192,347 claims, but settled just 27,911 of them with a total liability of nearly $1.2 billion. The trust has paid out just $700 million of that.

Nearly all were halted in July 1990, when a federal judge ordered an overhaul to stop the trust from hemorrhaging assets designed to meet worker health claims for decades.

A restructuring plan that pays the sickest claimants first - rather than on a first-come, first-served system - and ties the trust closer to Manville Corp. was approved last year. A federal court appeal is pending.

If upheld, the plan still could face a Supreme Court appeal, further delaying payments to victims, many of whom have died awaiting compensation.

The trust had depleted its cash until it faced running out of money for future claims. It blamed inaccurate estimates of the number of claims and settlement values - $25,000 compared to actual average payments of $43,000.

Under the new system, no claimant will get more than 45 percent of a settlement until all cases are resolved, and no one will be paid until two- thirds of the most serious cases are settled. Under a staggered process, initial payouts are expected to be just 12 percent of settlement value.

The new scheme makes litigation a last resort. As part of the restructuring, U.S. District Judge Jack Weinstein dismissed all lawsuits against the trust, most of which centered on long delays in settlement.

''The trust is taken out of the crucible of litigation and put basically into an alternative dispute resolution mechanism,'' said Les Fagen, who represents future claimants. ''Just inherently people won't be at each other's throats.''

The trust, based in Washington, is receiving about 1,500 new claims monthly. David Austern, its general counsel, said 220 emergency claims worth $6.75 million have been paid during the freeze.

The trust's previous board and executives were criticized for failing to control the cash outflow and enormous litigation expenses. The failure led to appointment of Falise and two other new trustees.

The trust currently has $144 million in cash, $1.725 billion in Manville bonds and $756 million, or 80 percent, in Manville stock, for total assets of $2.6 billion. But its present and future liabilities are estimated as high as $8.5 billion.

The trust will receive 20 percent of Manville's annual net profits for as long as needed, and up to $520 million in special payments over seven years.

A Lehman Brothers study issued in January estimated the trust could face 210,000 more claims. Since asbestos-related diseases can take decades to appear, claims are not expected to start declining until at least 1998. To meet future payments, the trust has to maximize its return on Manville holdings.

Because the trust's future is closely tied to Manville's performance, it plans to take a more active role in the company's affairs.

The trust has hired Goldman, Sachs & Co. as financial adviser, and Falise said the firm evaluated Manville's announced purchase last week of Macon Kraft Inc., a Georgia company that makes paper containers.

Manville, based in Denver, specializes in fiberglass and forest products. Like most companies, Manville stopped using asbestos in the 1970s.