The strike in public hospitals provoked the suspension of 1,030 medical appointments, 229 specialized procedures and 114 surgeries.
Health Minister Fernando Llorca Castro will replace Sáenz starting Thursday and Vice Minister María Esther Anchía will temporarily work as Health Minister.
Union leaders demanded that President Luis Guillermo Solís ensure the immediate dismissal of Caja Executive President María del Rocío Sáenz Madrigal.
Caja Pension Manager Jaime Barrantes said they will evaluate the unions' petition along with others that they have received from other groups in recent days.
Union leaders hope to block vehicle traffic along the capital’s Second Avenue, in front of the Caja’s main building, to get the institution's attention.
May Day in Costa Rica brought together protesters from public workers unions and a wide variety of other groups, including students, sex workers and indigenous people.
Costa Rica's President Luis Guillermo Solís on Wednesday denied that he or anyone else from his administration had previously reached an agreement with public unions over a national strike held last Monday.
Union leaders on Monday will request a 2 percent increase in private-sector wages for the second half of this year, at a 4 p.m. session of the Labor Ministry's National Wages Council.
Costa Rican President Luis Guillermo Solís has won perhaps one of his biggest challenges to date, as lawmakers on Thursday struck down three separate proposals to slash the administration's ₡7.9 trillion ($14.5 billion) budget proposal for 2015.
About 150 people turned out Monday to a protest called by the National Association of Public and Private Employees (ANEP) against proposed cuts to the national budget for 2015.
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