The United States will provide half of an emergency loan of $1.85 billion agreed on yesterday between financially troubled Mexico and 12 industrialized countries, the Federal Reserve announced.

About one-third of the total, arranged through the Bank for International Settlements in Basel, Switzerland, was made available immediately, sources said.

However, governments and commercial banks that Mexico has asked for cash are linking their aid to Mexico's agreement with the International Monetary Fund on austerity measures aimed at restoring financial health. Mexico has asked the IMF for a loan of up to $4.8 billion, $4 billion of which would be tied to policy conditions such as curbing public spending and borrowing.

Commercial banks have agreed in principle to renew loans to Mexico that fall due before the end of November. However, the details of the renewals -- including the interest rate Mexico will have to pay when its debts are rolled over -- have not yet been settled, banking sources said.

Mexico has a debt of $80 billion, $20 billion of it owed to U.S. banks, sources say. Private companies in Mexico owe foreigners just over $22 billion of the $80 billion, sources said, with the rest owed by the government.

There are several hundred banks worldwide with money at risk, ranging from major international banks to small regional and local banks in the Southwest United States. An advisory group of 14 big banks has been set up to head the negotiations with the Mexicans.

The emergency cash made available through the BIS will come in three installments, each for three months, sources said yesterday. Mexico requested the money as soon as possible, and the BIS has reportedly agreed to provide the second two portions this month.

However, the countries joining in the loan made it clear that they wanted Mexico to reach agreement with the IMF. The cash "provides for drawings by Mexico in line with progress toward agreement between Mexico and the IMF," the announcement of the loan said

A run on the Mexican peso, which has plummeted against the U.S. dollar, pushed Mexico to the edge of bankruptcy in the middle of August. Since then, officials in various countries and international organizations, led by the United States, have scrambled to put together a package to bail out Mexico while it negotiates to stretch out its heavy loan payments to commercial banks and a longer-term loan from the IMF.

The Mexicans have said they expect $500 million to $1 billion in new money from their bankers within the 90-day grace period on loan repayments, but bankers say there is no way that money will be in transit until Mexico signs an agreement with the IMF and the banks are satisfied.

The advisory group is now meeting with the Mexicans to "pull together" key figures on cash flow, what payments will be met, and the level of the Mexican foreign exchange reserves during the next 90 days, one banker said yesterday, adding that these are "all the things Mexico historically has not been very candid about."

One banker commented, when told that the U.S. Treasury expects banks to agree to send new money soon, "Maybe the Treasury doesn't know what's going on.

" The Mexicans' immediate needs are satisifed to a pretty good degree by the government-to-government aid and the 90-day postponement of principal repayments to the commercial banks," the banker said. However, an adminstration official said, "I think there's a fair amount of bargaining going on. . . . I think everyone expects that the banks have to come up with new money in the next 90 days" just so that Mexico can meet interest payments and pay for its imports.

The banks are just trying to get the best deal on the new money, he said.

The countries joining in the BIS loan were Belgium, Canada, France, West Germany, Italy, Japan, Netherlands, Sweden, Britain and two non-BIS members, Spain and Switzerland. Of the U.S. money, $600 million will come from the Treasury and $325 million from the Fed. The United States agreed to match the money put up by the Europeans.

In California, White House spokesman Larry Speakes said that President Reagan was briefed on the crisis and agreed that the United States would "do what we can to be helpful."