In 1421 the Romans gave asylum to a pretender to the Ottoman throne, Prince Orhan. They believed that by doing so they could conspire to undermine the Ottomans from within, since they weren't strong enough militarily to do this. Sultan Murad II marched his army to Constantinople and demanded that Orhan be handed over to him, but the Romans discreetly released Murad's younger brother Mustafa into Asia Minor to start a rebellion against the sultan. Murad diverted his army into Asia Minor, defeated and then executed his brother. While this was happening the Romans began bribing Sultan Murad's chief vizier Halil Pasha to convince the sultan to leave the Romans alone. Halil managed to do this by convincing Murad that if he conquered Constantinople he'd risk uniting the rest of Christendom against him in a crusade. Murad reluctantly adopted a policy of tolerance and co-existence with the Romans for the rest of his life. For the next thirty years Murad paid the Romans an annual subsidy to cover the cost of Orhan's "stay" in Constantinople (which basically became an unofficial detainment). The two parties reached an agreement that worked for both of them.

When Sultan Murad died in 1451, he was succeeded by his son Mehmed (who murdered his brothers on his way to power), who was an altogether more short-tempered, volatile and aggressive man. Sultan Mehmed II was convinced by his military advisors to abandon his father's policy of tolerance towards the Romans. They insisted he was destined to be a great empire-builder like Alexander, and that it was his holy duty to wage jihad against the Christians. Mehmed may have been a warlike man, but he was also cautious, and he spent a long time studying the defences of Constantinople and formulating plans on how to conquer it. In the meantime a casus belli presented itself to him quite conveniently.

The new Roman Emperor, Constantine XI (destined to be the final one), tried to extort more money out of the Ottomans by threatening to release Orhan if the Sultan didn't raise the annual payment. Halil Pasha, who once convinced Murad to be tolerant and patient with the Romans (he was the lone voice to do so), was furious when he received this threat and instantly dropped his support of the Romans, sending this letter in response:

You stupid Greeks, I am sick of your devious ways. The last Sultan was a lenient and conscious friend to you. The present Sultan is not of the same mind. You are fools to think you can frighten us with your fantasies, and that when the ink on our recent treaty is barely dry. We are not children without strength or reason. If you think you can start something, do so. If you want to proclaim Orhan as Sultan in Thrace, go ahead. If you want to bring the Hungarians across the Danube, let them come. If you want to recover the places you lost long since, try this. But know this: you will make no headway in any of these things. All that you will achieve is to lose what little you still have.

Halil Pasha presented the Romans' threat to Sultan Murad, who realized that this threat - which was in reality a poorly conceived bluff on the part of Constantine for more money - gave him the perfect casus belli which would justify declaring war on his own vassal. After more planning and preparation, he assembled his huge army and marched on Constantinople. The only person that could have convinced him not to do so was Halil Pasha, who Constantine had alienated with his poorly thought out threat. When the Sultan's armies were gathered outside Constantinople, Murad sent a simple demand to Constantine: "Surrender the city, or stand and do battle." Constantine refused to surrender and prepared for the fateful siege.

Source: Ghost Empire by Richard Fiddler