MEXICO CITY (AP) _ Mexican currency markets reopened nervously Monday after plunging more than 20 percent last week in a stunning dive that analysts blamed on the economy's uncertain outlook.

The peso's value held steady during the morning, began slipping at midday but then strengthened at some commercial banks.

Private exchange houses in Mexico City opened their windows to offer 715 pesos to customers who wanted to trade a U.S. dollar on the free market. For those wanting to buy a dollar, the cost was as much as 745 pesos.

By midday, the rates were 735 and 765. Commercial banks gave 730 pesos for a dollar and demanded 735 pesos for those wanting to buy one.

Later in the afternoon, it strengthened to 712 and 718 at some commercial banks.

A week ago, the rate was 554 and 559.

In El Paso, Texas, along the U.S.-Mexico border, private banks on Monday quoted rates of 700 and 735, up from 660 and 690 at the end of the last week.

The decline in the free-market rate, which is used in tourism and for most border transactions, means travelers visiting Mexico can get more pesos for their dollars this week than last. Mexicans, though, have to come up with more pesos if they want to buy dollars.

The value of a second rate, regulated by the government, slid gradually last week, standing at about 546 pesos to the dollar on Monday. This rate, set daily by representatives of the nation's central bank and commercial banks, is used in about 80 percent of commercial transactions.

Currency traders and other analysts said the peso plunge was sparked by investors nervous about a string of bad economic news. In shaky economic times, investors often trade their own weaker currencies for stronger ones like the dollar.

An official at the Bank of Mexico, the central bank, said that ''there's always concern'' in the government about such sharp declines.

But the official, who spoke on condition of anonymity, said the central bank ''is not going to intervene in the free market. Let it get wherever it wishes.'' In the past, analysts suspected that the central bank was directly or indirectly supplying dollars to the currency markets to support the peso. The central bank denied it was taking such action.

Treasury Secretary Jesus Silva Herzog said over the weekend that the government would have something to say shortly about the deterioration of the peso.

In Basel, Switzerland, it was reported that Miguel Mancera, head of the central bank, canceled long-standing plans to attend the annual meeting of the Bank for International Settlements. The meeting is a prestigious event and one of the few times when central bankers from developing countries can meet their counterparts from key industrialized nations.

Mancera's decision not to attend was viewed in Switzerland as another sign of Mexico's worsening situation. But the central bank official in Mexico City said, ''He simply decided not to go.''

Among the factors making investors nervous about the economy is the government's inability so far to work out a new financial aid package with the International Monetary Fund and foreign bankers.

The government needs the aid to help it meet payments on its $97.6 billion foreign debt, the second highest in the developing world after Brazil.

Silva Herzog raised the possibility late last week in an interview with The Associated Press that Mexico might suspend payments on the debt if the negotiations were not successful.

Moreover, there have been reports in local newspapers - repeatedly denied by government officials - that the administration of President Miguel de la Madrid is set to unveil a series of measures that will deliver strong medicine to the ailing economy.

One currency trader, who also asked not to be identified for business reasons, said these factors as well as reports of divisions within de la Madrid's Cabinet over economic action have contributed to a lack of confidence in the government. Such unease, he said, has caused turmoil in the market.

In addition, the government reported last week that consumer prices surged 5.6 percent in May, giving an accumulated inflation rate of 32.1 percent for the first five months of the year.

As a result, analysts predict the yearly inflation rate will top the 63.7 percent registered last year. It was 59.2 percent in 1984.

Mexico's economic woes were aggravated early this year by the sharp plunge in world oil prices. Mexico, the world's fourth-largest oil producer, earns about 70 percent of its foreign income from crude sales.

With the fall in oil prices, government officials estimate earnings this year will be clipped at least in half from the $13.3 billion of last year.

The peso has weakened sharply in recent years. In February 1982, it was 26 to the dollar. It was 445 to the dollar at the start of 1986.