All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Offering the two-Rak‘ah prayer before the obligatory Fajr prayer is not obligatory; however, it is one of the most important and confirmed Sunnah prayers. The Prophet, sallallaahu ‘alayhi wa sallam, used to observe it keenly and did not neglect it whether in residence or travel. It was narrated that ‘Aa'ishah said, "The Prophet, sallallaahu ‘alayhi wa sallam, was never more regular and keenly persevering in offering any Nawaafil (i.e. Sunnah prayers) than the two Rak‘ahs of the Fajr prayer." [Al-Bukhari and Muslim]
Although the Prophet, sallallaahu ‘alayhi wa sallam, keenly observed these two Rak‘ahs of prayer, ‘Aa'ishah still called them Nawaafil; i.e. supererogatory and not obligatory.
This is the view of the vast majority of early and later scholars. Al-Hasan Al-Basri though, held that it is obligatory, as was cited in Al-Musannaf by Ibn Abu Shaybah. Ash-Shawkaani was also inclined towards this view, as was underlined in his book Nayl Al-Awtaar. He relied on the hadeeth reported on the authority of Abu Hurayrah that says that the Prophet, sallallaahu ‘alayhi wa sallam, said, "Do not leave the two Rak'ahs of Fajr (meaning the Sunnah of Fajr prayer), even if you were being pursued by cavalry." [Ahmad and Abu Daawood] Al-‘Iraaqi commented on this hadeeth saying, "This hadeeth is adducible (or acceptable)." However, Al-Albaani classified it as weak.
Even if this hadeeth is proved to be authentic, it is interpreted to indicate encouraging and urging Muslims to offer the two Rak‘ahs before the Fajr prayer and not to mean that they are obligatory. This is because it has been authentically reported in Saheeh Al-Bukhari and Saheeh Muslim that the Muslim is enjoined to offer five obligatory prayers only throughout the day and night. Talhah ibn ‘Ubaydillaah reported:
"A man with disheveled hair, one of the people of Najd, came to the Messenger of Allaah, sallallaahu ‘alayhi wa sallam. We heard the humming of his voice but could not fully understand what he was saying, till he approached close to the Messenger of Allaah, sallallaahu ‘alayhi wa sallam. Then I came to know that he was asking about Islam. He, sallallaahu ‘alayhi wa sallam, said, 'Five daily prayers during the day and the night.' The man asked, 'Am I obliged to perform any other prayers besides these?' He, sallallaahu ‘alayhi wa sallam, replied, 'No, unless you perform more voluntarily (Nawaafil).' The Prophet, sallallaahu ‘alayhi wa sallam, then informed him of the obligatory fasting in the month of Ramadan. The man asked, 'Am I obliged to fast anything else besides this?' He, sallallaahu ‘alayhi wa sallam, said, 'No, unless you do more voluntarily.' The Prophet, sallallaahu ‘alayhi wa sallam, informed him of the obligatory zakah. The man asked, 'Am I obliged to pay anything else besides this?' The Prophet, sallallaahu ‘alayhi wa sallam, said, 'No, unless you spend more voluntarily.' The man turned to leave while saying, 'By Allaah, I would neither make any addition to this, nor will decrease anything out of it.' The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said, 'He will succeed if he is sincere (i.e. if he is saying the truth, he will succeed),' or, 'He will enter Paradise if he is sincere.'" [Al-Bukhari and Muslim]
Allaah knows best.