Taking a look on a good number of interpretation books around these verses, some have considered those cited in these verses to be the people of book who have accepted Islam, and some have considered them to be the true believers among the people of book (submitted to Allah and not their own desires).
But in one book I found an explanation that clarified the situation better: In the verses prior to these verses Allah was describing the worse situation of the wrongdoers of the people of the book, then in these verses He state not all of the people of the book are such, so that the main problem with the people of the book cited in previous verses is their wrong deeds and intentions not them being worse humans in creation and blow. There are witnesses in Quran that such good will people of the books as cited in these verses are believers anyway and if they are informed of Islam they will accept it as well (stress on their good will), they wish to be good persons and even hasten to good deeds, so why not to admit the book revealed from their Lord? This last explanation can nicely bring the first two different interpretations in one understandable place. Now "reciting the verses of Allah" can point to either Bible or Quran depending on them being informed of Islam or not.
Some of the books I referred to:
- تفسیر نمونه، آیت الله ناصر مکارم شیرازی
- المیزان فی تفسیر القرآن، علامه سید محمد حسین طباطبایی
- الأصفی فی تفسیر القرآن، ملا حسن فیض کاشانی
- اطیب البیانفی تفسیر القرآن، سید عبدالحسین طیب
- انوار التنزیل و اسرار التأویل، عبدالله بن عمر بیضاوی
- البحر المحیط فی تفسیر، ابوحیان محمد بن یوسف اندلسی
- البلاغ فی تفسیر القرآن بالقرآن، محمد صادقی تهرانی
- التبیان فی تفسیر القرآن، محمد بن حسن طوسی