The chief executives of Texaco Inc. and Pennzoil Co. met yesterday and agreed to renew negotiations on a settlement of Pennzoil's $10.53 billion judgment against Texaco.

Neither side would provide details of the two-hour meeting between Pennzoil Chairman J. Hugh Liedtke and Texaco Chairman John McKinley, held at an undisclosed location in New York City. "They agreed to continue meeting," a Pennzoil spokesman said.

Pennzoil's chief trial counsel, Joseph Jamail Jr., said he had talked to Liedtke after the meeting. "He was not optimistic. He was not pessimistic. He was hopeful," Jamail said.

Settlement negotiations should begin soon, presumably involving the teams of corporate officials, lawyers and investment bankers who had tried to reach a settlement before talks broke off in January.

The collapse of those initial settlement efforts left bitterness between Texaco and Pennzoil that neither tried to conceal.

Some details from those negotiations made it clear how far apart the two sides are. Texaco offered to buy Pennzoil, an offer that Liedtke has flatly rejected.

According to Jamail, Texaco's proposal "wasn't an offer. It was an insult. They wanted to buy Pennzoil for less than it's worth, with zero for the settlement.

"Nothing is going to happen until Texaco takes some reality pills and says, 'Here is X dollars,' " Jamail said.

"It takes two" to negotiate, a Texaco source said recently. "They have not been forthcoming at all."

The two companies have been in conflict for more than two years, after Texaco outbid Pennzoil for control of Getty Oil Co. A Texas jury last year ordered Texaco to pay Pennzoil $10.53 billion -- including $3 billion in punitive damages -- after concluding that Texaco had intentionally violated Pennzoil's rights in the bidding for Getty.

But the climate for negotiations apparently has improved as the dispute entered a new legal phase, said some sources close to the companies and outside observers.

The meeting between McKinley and Liedtke coincided with the end of a standstill order imposed last year by Texas State Judge Solomon Casseb Jr., who presided over the trial. The order barred Texaco from disposing of or encumbering its assets and restrained Pennzoil from attempting to file liens against Texaco's property or taking other action to enforce the judgment.

But Texaco remains similarly protected under a federal court order that will be in effect until Texaco has exhausted its appeals.

There is no specific restriction in the order barring Texaco from using some of its assets as collateral to obtain additional financing, but a Texaco source said, "Texaco has no intention of dissipating any assets."

According to outside observers, Texaco won an important round in the conflict in obtaining the federal court protection.

But Texaco's appeal of the jury verdict in Texas courts opens a new round with an uncertain outcome, giving both sides more of an incentive to seek an out-of-court settlement, said an attorney for one of the companies.

Texaco is pressured by the clock -- the interest it owes Pennzoil on the uncollected judgment is mounting at $3 million a day. And Texaco's lenders still are "on notice that you loan money to Texaco at your peril, because we assert our right to go first" in claiming a right to Texaco's assets, Jamail said.

Pennzoil must weigh the risk that a state appellate court may substantially reduce the size of Texaco's judgment from the current amount of $10.53 billion plus interest, said Alan Edgar of the Dallas investment banking firm Schneider, Bernet and Hickman.