The Meeting of the Two Parties, Musa's Propagation of the Message and the Magicians
Allah, the Exalted informs that when Fir`awn and Musa agreed to an appointed meeting at a specified place and time, Fir`awn began to gather some magicians from the cities of his kingdom. Every person who had any affiliation with magic at that time was summoned, and magic was very widespread and in demand at that time. This is as Allah says,
(And Fir`awn said: "Bring me every well-versed sorcerer.") 10:79 Then, the day came. It was the day when all of the people gathered, which was well-known, being the day of the festival. Fir`awn was there sitting upon his throne surrounded by the elite officials of his kingdom. The subjects were all standing on his right and his left. Then, Musa came forward leaning upon his stick accompanied by his brother Harun. The magicians were standing in front of Fir`awn in rows and he was prodding them, inciting them and encouraging them to do their best on this day. They wanted to please him and he was promising them and inspiring them. They said,
فَتَنَازَعُوا أَمْرَهُم بَيْنَهُمْ (then, they disputed among themselves in their matter - 20:62), وَأَسَرُّوا النَّجْوَىٰ (and kept their talk secret - 20:62). Ultimately their unanimous decision was to proceed with the contest because, in their opinion, Sayyidna Musa (علیہ السلام) and Sayyidna Harun (علیہ السلام) were both magicians who wished to drive away the Pharaoh and his men from Egypt by their magic and to eradicate their ideal way of life. This decision of theirs is mentioned in verse 63 in the following words:
Tazkirul Quran
Maulana Wahiduddin KhanOn ayahs 61–63
Pharaoh sent his messengers throughout the country with an invitation to all the expert magicians. When they had gathered at the fair grounds, before the start of the contest, Moses made a speech. This speech was nothing new to the people; it was in the nature of a reminder. The magicians and other people were already aware of what Moses’ message was going to be. They knew that Moses upheld the unity of God as opposed to the belief in a multiplicity of gods, or in the existence of partners to God. Against this background, Moses took this last opportunity to give the final admonition. He impressed upon Pharaoh and the magicians how vital it was not to treat this as mere conjuring. He said that it was an extremely serious matter to treat any sign from God as if it were magic and then to try to surpass it by human sleight of hand. This amounted to an attempt to counter actual reality by means of an absolutely unreal thing; this would certainly result in destruction. He clarified that while they were apparently bent on proving him false, what they were doing in reality, was trying to prove the falsity of God Himself. Those who give free rein to this type of arrogance can never succeed in the world of God.
Uthmani text of the Madinah mushaf (King Fahd Complex). Translation: Saheeh International. Tafsir via Quran.com.