Greeks have a similar expression for demurring when thanked for something or complimented: 'Na 'sai kala' (or, in the plural/formal usage, 'Na 'ste kala'), which means, literally, 'May you be well'. When uttered in response to a compliment, it can be an expression of shyness or reluctance to hear praise.
The same words are used sometimes as the end of a telephone conversation, or at the end of a visit. Other words said to those who are departing are 'Sto kalo' or 'Na pas/pate sto kalo' (which means literally, 'Go to the good'.
Thank yous are also frequently deflected by Greeks with the word 'Tipota', which means 'nothing', much like the English expression, 'Think nothing of it,' or, 'It was nothing'., or 'Don't mention it'. Many will also respond to expressions of gratitude with the words, 'Sto theo' ('to God', meaning.'Thank God, not me', with the implication that everything comes from God. 'Ta Leme' is one that means we'll speak soon.