The healthcare union's chairman Valdis Keris told the press Tuesday that an emergency meeting of the union's council will be held, where it will decide on a no-confidence vote against Māris Kučinskis.
The medics demand healthcare funding to reach 3.2% of GDP in 2017 and 3.5% of GDP in 2018. Latvia's current healthcare spending is 3% of GDP.
Kučinskis told Latvian Radio that he had met medics' organizations and their views had "come a bit closer".
If medics ask him to step down, however, Kučinskis said, "I won't stop working".
The Cabinet of Ministers Tuesday approved the government's action plan on what Latvia has to do to promote Latvia's economic growth.
Healthcare unions criticized the plan, saying that it does not include a specific increase in healthcare funding.
Kučinskis also used the interview to defend the plan, saying it does not lack focus as "this is a plan of action, not a budget."