Photographed in Lybia, Marsa El Brega, 17th January, 2014. This plant is quite similar to Anagalis arvensis. However, the flowers are 2x larger and dark blue. The plant is also significantly larger than Anagalis arvensis.
In spite of the mystery solved, it seems that the flowers are rather big for A. arvensis ssp. foemina. What about Anagallis monelli syn. A. linifolia? On the other hand the leaves in this case should be narrower with acute apex.
I evaluated your answer with one point because I am not able to give 2 points. You have a very strong observation. It is not visible on the photo, but I could confirm, the size of the flower 2x or even 3x larger than the common European weed A. arvensis.
The petals are rather broad and overlap one another. That's not typical for A. foemina. It is possible that this is one of the mediterranean forms of A. arvensis, what has been called A. arvensis subsp. latifolia. This very often is blue flowered and also has bigger flowers than A. arvensis from Central Europe. I don't know A. monelli very well, but it should have the biggest flowers. You may try the key in Flora Iberica: http://www.floraiberica.es/floraiberica/texto/pdfs/05_080_09%20Anagallis.pdf