The Borders MSP and MP have urged Humza Yousaf to provide more funding to prevent cuts to local health services.
Recently, NHS Borders said they would need to make £28 million of cuts to services over the next year because of a growing financial deficit.
NHS Borders Chief Executive Ralph Roberts said the situation is "clearly unsustainable".
Rachael Hamilton MSP and John Lamont MP said the crisis at NHS Borders could no longer be "ignored" by the SNP Government.
They wrote to First Minister Humza Yousaf urging him to intervene to prevent service cuts.
In a joint letter, Rachael Hamilton MSP and John Lamont MP said: "Local health services are already in crisis. Constituents write to us on a regular basis because they are struggling to access GP and dentist appointments. We hear from local people who have waited months, sometimes even years, for essential treatment. Referrals for conditions such as cancer and mental health treatment are slower than they should be given the potential repercussions of late diagnosis.
"The NHS in the Borders needs investment to improve its services. Cuts will only make the crisis worse.
"Local people are deeply troubled by the possibility that healthcare services will become very difficult to access quickly.
"We urge you to step in with extra funding to allow NHS Borders to at least maintain the services it currently provides.
"The Borders cannot afford to be ignored by the SNP Government any longer."