Mexico has obtained commitments for $4.3 billion of the $5 billion its private bankers are supposed to lend under terms of an agreement the country signed with the International Monetary Fund.

Officials of Citibank and Bank of America, which are coordinating bank lenders to Mexico, said replies are continuing to come in from the more than 1,000 banks around the world that are Mexican lenders. Mexico, which owes more than $80 billion to foreign governments and Mexican bankers, has asked its banks for easier terms on much of the debt that is outstanding, as well as $5 billion in new loans in 1983.

Meanwhile, the International Monetary Fund yesterday approved a $546 million loan to Brazil to help cover a shortfall in its export earnings during the past year.

The loan is separate from a $4.9 billion loan package the IMF earlier had tentatively approved for Brazil to help it meet its international debts over the next three years. That larger loan still awaits formal approval of the IMF's board of executive directors.

The loan approved by the board yesterday will be made under the IMF's compensatory financing facility, set up to deal with export shortfalls of developing countries.

On Monday, Brazil, which also owes about $80 billion, asked its banks for easier terms on $4 billion in loans that come due in 1983, as well as for an additional $4.4 billion in new loans next year.