His fourth minister of economy, Domingo Cavallo, was appointed in 1991, and deepened the liberalization of the economy. The Convertibility plan was sanctioned by Congress, setting a one-to-one fixed exchange rate between the United States dollar and the new Argentine peso, which replaced the Austral. The law also limited public expenditures, but this was frequently ignored. Under Cavallo, there was increased free trade, alongside a general reduction of tariffs on imports and state regulations to tackle inflation, and high taxes on sales and earnings to reduce the deficit caused by it. Initially, the plan was a success: the capital flights ended, interest rates were lowered, inflation fell to single digits, and economic activity increased; in that year alone, the gross domestic product grew at a rate of 10,5%.
Antonio Cafiero, a rival of Menem in the PJ, was unable to amend the constitution of the Buenos Aires province to run for a re-election. Duhalde stepped down from the vice presidency and became the new governor in the 1991 elections, turning the province into a powerful bastion. Menem also selected famous people with no political background to run for office in those elections including the singer Palito Ortega and racing driver Carlos Reutemann. The elections were a big success for the PJ. After these elections, all of the PJ was aligned with Menem's leadership, with the exception of a small number of legislators known as the "Group of Eight". The opposition from the UCR was minimal, as the party was still discredited by the 1989 crisis. With such political influence, Menem began his proposal to amend the constitution to allow a re-election. The party did not have the required super majority in the Congress to call for it. The PJ was divided, as other politicians intended to replace Menem in 1995, or negotiate their support. The UCR was divided as well, as Alfonsín opposed the proposal, but governors Angeloz and Massaccesi were open for negotiations. The victory in the 1993 elections strengthened his proposal, which was approved by the Senate. Menem called for a non-binding referendum on the proposal, to increase pressure on the radical deputies. He also sent a bill to the Congress to modify the majority requirements. Alfonsín met with Menem and agreed to support the proposal in exchange for amendments that would place limits on presidential power. This negotiation is known as the Pact of Olivos. The capital city of Buenos Aires would be allowed to elect its own chief of government. Presidential elections would use a system of ballotage, and the president could only be re-elected once. The electoral college was abolished, replaced by direct elections. The provinces would be allowed to elect a third senator; two for the majority party and one for the first minority. The Council of Magistracy of the Nation would have the power to propose new judges, and the Necessity and Urgency Decrees would have a reduced scope.
In 1991 Menem became the first Head of State of Argentina to make a diplomatic visit to Israel. He proposed to mediate between Israel and Syria in their negotiations over the Golan Heights. The diplomatic relations were damaged by the lack of results in the investigations over the two terrorist attacks.