Government and private analysts yesterday hailed the agreement that Mexico reached with the International Monetary Fund on a new loan package as a potential turning point in the Third World debt crisis, and as the first successful application of the Baker debt initiative.

The general reaction in Washington yesterday was that the new and more generous terms hammered out between Mexican government officials and the IMF may restore economic growth and -- equally important -- give Mexico a necessary injection of financial stability.

Sen. Bill Bradley (D-N.J.), who has criticized the Baker plan and instead called for substantial debt relief, said in a telephone interview, "This could be a step in the right direction, depending on how the banks respond. My sense is that they the Mexicans are anticipating some interest-rate relief, and that the administration is finally coming to understand that we have a strategic opportunity here in trying to help Mexico restore growth."

He added that it is significant that the total aid package "appears to be twice as big" as the amounts mentioned before. "We have yet to see whether there is a new mood in this proposal that recognizes a spirit of partnership; if that's there, it's encouraging," Bradley said.

Richard Feinberg, a specialist on Third World debt problems for the Overseas Development Council, also applauded the agreement. "If the IMF and others succeed in putting together a multi-year package for Mexico with some flexibility to reflect changing economic conditions, that would be a major event," Feinberg said.

But to some extent, the relative euphoria over the Mexican deal was dampened by an apprehension that Peru will default on a $180 million payment due the IMF on Aug. 15. If that occurs, Peru will be declared ineligible for further IMF assistance. That would represent an unprecedented rupture in the international financial system.

An IMF source who insisted on anonymity acknowledged that the international lending agency had made a dramatic departure from its earlier demands on reduction of Mexico's budget deficit. He said that the new deal could be viewed as a first major success for the Baker plan, provided the commercial banks go along.

The IMF modified its usual stance, he conceded, because "the Mexicans are so beset with the price of oil -- it dropped so much in such a short span of time -- that unless we give them a chance to breathe, they will stop breathing. And if they stop breathing, they will stop paying."

The critical compromise made by the IMF was to accept the Mexican proposal that its budget deficit be cut to 10 percent of its gross national product by the end of 1987, rather than to 5 percent -- the original IMF target. IMF negotiators were concerned by the threat of inflation.

Treasury Secretary James A. Baker III had proposed his debt initiative in October. It called for an additional $9 billion in multilateral development bank loans and $20 billion in additional commercial bank loans over three years for 15 major debtors, including Mexico, provided the debtor nations adopt basic domestic economic reforms.

The proposed agreement signed yesterday, covering the balance of 1986 and 1987, would involve $1.5 billion in IMF loans to Mexico, more than $2 billion multilateral development bank (MDB) loans, and possibly up to $7 billion in new commercial bank money. The MDB loans would be mostly from the World Bank, with a small contribution from the Inter-American Development Bank.

In exchange, Mexico would agree to cut its budget deficit, liberalize foreign trade and encourage new foreign investment. These elements of economic reform, projected over a three-year period, match those that Baker had suggested precede the infusion of new capital from abroad.

But there are additional innovative elements in the aid package, notably a direct understanding that Mexico cannot be expected to absorb by itself the shock of the oil price collapse.

Therefore, the program guarantees Mexico additional IMF/World Bank help if the price of oil falls below the present $9 to $14 a barrel, and if Mexico's economic growth targets of 3 to 4 percent by early 1987 are not met.

Treasury Undersecretary Richard Darman said in a telephone interview that among the potential Baker initiative countries, Mexico had proved "the hardest to deal with," but that the solution "is among the most innovative."

Darman pointed out that the program is oriented toward a resumption of economic growth in Mexico through structural reforms, not conventional austerity. In addition, the plan provides a significant real improvement in IMF and bank coordination, as well as an increase in the IMF's "time horizon" beyond a one-year standby program.

The key remaining questions, of course, are the amount of money -- and the terms -- to be offered by commercial banks. The IMF is anxious to see the full program in place before giving way to unreserved cheering, and there are some doubts that the banks will put up as much as the reported $7 billion.

In principle, when they endorsed the concept of the Baker plan, the commercial banks said they would offer fresh money to the 15 nations when they made significant reforms, and when the IMF and World Bank instituted an overall program that makes economic sense.

"Much depends on whether the commercial banks come through," said C. Fred Bergsten of the Institute for International Economics.