MEXICO CITY, NOV. 19 -- The troubled peso plunged further in free trading here today while the stock market surged boldly ahead, with the biggest gainers those companies heavily dependent on export sales.

When trading closed this afternoon, the peso stood at 2,550 to the dollar, 49 percent below the 1,715-peso rate in effect when trading opened Wednesday morning. During the day Wednesday, the central bank decided to withdraw financial support from the currency.

The Mexican stock market, meanwhile, registered a strong 17.5 percent gain today, building on Wednesday's record 18 percent rise. While exporters gained strongly, the big losers were the department store chains whose imports will be made more costly by the falling peso.

Officials at Mexico's central bank stressed that the peso's fall affected only the free-exchange rate. The "controlled" exchange rate, fixed daily by the central bank and used for more than two-thirds of Mexico's foreign exchange transactions, was set this morning at 1,710 to the dollar, down only slightly from Wednesday's 1,706.

Treasury Secretary Gustavo Petricioli, speaking before Congress today, said the Mexican economy is fundamentally sound and promised that the government's exchange rate policies will remain "rational and flexible."

Petricioli said today that Mexico still has $15 billion in foreign exchange reserves, a Latin American record. Officials interviewed said they intend to keep reserves at that level in coming months to protect against international economic turmoil.

The recent pressure on the peso was the result of an "abnormal, transitional, temporary" surge in capital flight and dollar purchasing for private foreign debt payments, Petricioli said. Quashing speculation, Petricioli explicitly ruled out the imposition of strict new foreign exchange controls, saying such rules are "impossible" to enforce in a country bordering the United States.

Even though Mexican officials today were predicting a short-term recovery in the free peso rate, they said this week's fall should help keep dollars from flowing out of the country. The sharp recent drop in the Mexican stock market -- the index had fallen by 70 percent since early October, wiping out the gains of what had been 1987's fastest-growing national stock exchange -- had started a new round of capital flight, they said.

Though certain to exacerbate inflation and undermine confidence in the national currency, the peso's fall is good news to Mexican export manufacturers. Since the massive peso devaluations of the 1982 debt crisis, Mexico has tripled its sales of manufactured goods to more than $10 billion yearly, creating a powerful sector of the economy that benefits from cheaper currency.

The change in mood was evident in exchange houses in the downtown financial district. In a radical change from the nearly universal gloom that greeted devaluations in years past, many businessmen were openly delighted by the peso news. There was relatively little demand for dollars, traders reported, in contrast to the dollar-buying panic generated by earlier sharp peso falls.

"There has been an increase in the demand for dollars in recent weeks, but there isn't much demand today," Jose Osorio, the supervisor of a downtown exchange house run by a government bank, said Wednesday. "Everyone seems reasonably calm about this."

This optimism was not universal. Hugo B. Margain, a former Treasury secretary and now an influential ruling-party senator, called the peso's plunge "an indication that the Mexican economy has serious structural defects."

The economy's most persistent problem, it is widely agreed, is inflation. Running now at a record annual pace of 140 percent, inflation will accelerate further as the falling peso increases the cost of imports and debt service. Despite official assurances that the controlled exchange rate would continue declining only gradually, some retail prices began rising today as merchants anticipated higher stock replacement costs.