EU policy should focus more on preventing the spread of war in the countries from which people are fleeing she suggested - though she offered no concrete ideas as to how such a formidable task might be achieved, and made no mention of military intervention.
It is also necessary to prevent trafficking in human beings and to strengthen the EU's borders, she said, again without going into details.
Straujuma reiterated that Latvia's planned intake of 250 refugees over two yers would be a one-off event.
On the same morning broadcast, National Alliance MEP Roberts Zile expressed greater doubts, predicting that in fact many more refugees would end up in Latvia than the 250 stated.
He added that the overall refugee plan of European Commission head Jean-Claude Juncker was a complete flop.
The prospect of even a relatively small number of refugees arriving in Latvia has dominated the political landscape in recent weeks with illegal immigrants, economic immigrants and asylum seekers generally given the catch-all title of "immigrants".
A self-styled "anti-immigration" demonstration on August 4 brought several hundred people onto the streets of central Riga. While some expressed moderate views, others were explicitly racist.
The refugee issue has also increased tensions within the ruling three-party coalition.