It sounds like they are very shy and afraid of making mistakes, even though you've made an effort to make them feel comfortable. Some students just need a bit more encouragement. Do you speak their language? I have found that setting aside 5 minutes at the end of class for them to teach you words in their L1, and for you to practice simple phrases in their L1 helps them to see that you know what it's like to be a language learner too. You could have an agreement with your students - I'll learn 5 words of your language if you learn 5 words of mine.
The other thing I would recommend is to give them lots of support. Try choral reading - everyone reading the same thing at the same time. Repeat each reading several times to give them a chance to get used to it. You could also give them sentence frames. So, give them the whole sentence with one word missing and have them verbally fill in the missing word for you. E.g 'Today is (monday)'. Repetition will help them build up their confidence. Having everyone say the answer at once will also help. Another suggestion is to give them lots of opportunities to rehearse what they are going to say before they have to say it. So for example, if you are asking them to talk about their families, you could give them the vocabulary they will need (brother, sister, mother, father etc). Have them chorally practice saying those words. Then give them a sentence frame, eg 'I have two ______s'. Practice saying a sentence together a few times. Then have them work in partners to practice the sentence frames with each other, adding their own words ('I have a mother', 'I have two brothers', 'I have one sister' etc). Then have them say their sentence aloud to the class.
Lastly, you might want to give them some positive reinforcement - points or tokens for effort in English.
-Charlotte