Short answer
Yes. The hadith forbid praying at sunrise, noon and sunset, not reciting the Quran, so recitation is allowed at those times. Some Hanafi texts say that during those few minutes dhikr, dua and salawat are better than recitation, and if you recite an ayah of sajdah then, it is better to delay the prostration until the time passes.
Reciting the Quran outside salah at the three makruh times is permissible. Salah, including nafl prayer and sajdah tilawat for an ayah recited before that time, is not done in those times. Some Hanafi texts prefer dhikr and salawat to recitation in those moments.
The four schools agree on this.
Explanation
Uqbah ibn Amir said there were three times the Prophet ﷺ forbade them to pray or to bury their dead: when the sun is rising until it is up, when it is at its height until it passes the meridian, and when it is setting until it has set (Muslim). The ban is on salah. Nothing in the hadith forbids recitation, dhikr or dua at those times.
Practical points:
- You may keep reading your daily portion after Fajr straight through sunrise. Many people do their morning Quran then.
- If you reach an ayah of sajdah during those minutes, wait until the time has passed, then do the sajdah: see how to do sajdah tilawat.
- Once the sun is fully up (about 15 to 20 minutes after sunrise), you can pray ishraq.
- After Asr and after Fajr, nafl prayer is disliked, but recitation is not.
Some Hanafi references note that in the three times themselves, dhikr, dua and salawat are better than recitation. This is a matter of what is better, not of permission. The four schools agree that recitation is not forbidden.
For the exact times, see forbidden times for prayer.
The evidence
Sahih Muslim 831
Sahih... ثلاث ساعات كان رسول الله صلى الله عليه وسلم ينهانا أن نصلي فيهن أو أن نقبر فيهن موتانا ...
"There were three times in which the Messenger of Allah forbade us to pray or to bury our dead."
The prohibition at sunrise, noon and sunset is about prayer, not recitation.
Where the ruling is recorded
- al-Fatawa al-Hindiyya, Kitab al-Salah, chapter on the times of prayer, section on the disliked times. What is not done in the makruh times, and the preference for dhikr and salawat in them.
- al-Durr al-Mukhtar, Kitab al-Salah, the disliked times. Sajdah tilawat for an ayah recited earlier is not done in these times.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.