Victorian Premier Ted Baillieu and federal health minister Tanya Plibersek have had an unexpected encounter on the streets of Melbourne as the state's hospitals struggle to cope with millions of dollars in funding cuts.

Both politicians continue to blame the other for the financial strain on Victorian hospitals.

Instead of agreeing to meet on Tuesday while they were both in Melbourne, Ms Plibersek and Mr Baillieu chose to speak with the media.

The premier was giving a press conference just as Ms Plibersek walked by and entered the building he had just left.