N.M. Stat. § 37-1-16
Causes of action founded upon contract shall be revived by the making of any partial or installment payment thereon or by an admission that the debt is unpaid, as well as by a new promise to pay the same; but such admission or new promise must be in writing, signed by the party to be charged therewith. Such a cause of action shall be deemed to have accrued upon the date of such partial or installment payment, admission of indebtedness or promise to pay. Provided, that no admission that the debt is unpaid or new promise to pay the same shall be effective to extend the lien of any mortgage upon real estate or any interest therein given to secure the original indebtedness, unless the payment is accompanied by an admission or promise and unless such admission that the debt is unpaid or new promise to pay the same, signed by the party to be charged therewith and acknowledged by such party in the form prescribed by law for the acknowledgments of instruments affecting real estate, shall be filed for record in the office of the county clerk where said original mortgage is of record, prior to the date when any action to foreclose said mortgage lien would otherwise be barred under existing law; and provided further, that the foregoing proviso shall not be applicable to any recorded mortgage upon real estate or any interest therein until after three months from the effective date of this act.
NMS § 37-1-16