To clarify what the Gospel of Matthew is saying, in detail:
A. The Messenger of Allah (pbuh) said, "My likeness and the likeness of the prophets before me is like a man who built a house and completed it, except for one brick of it. So the people took to going around it and marveling at it, saying, 'If only you would place this brick!' I am that brick." [Sahih al-Jami` al-Saghir]
What the Messenger of Allah (pbuh) said agrees with what it says in the Gospel of Matthew: "Did ye never read in the scriptures, The stone which the builders rejected, the same is become the head of the corner: this is the Lord's doing, and it is marvelous in our eyes?"
B. The Arabs were disparate, warring tribes, without king, ruler, or chief, but after the arrival of this prophet, the Seal, Muhamad (pbuh), Allah (Mighty & Majestic) brought their hearts together and reunited them under the leadership of His prophet, Muhammad (pbuh) in whose message they believed and had faith. Thus the Muslims became a great nation, extending north and south, east and west, by the Bounty and Victory of Allah (Mighty & Majestic).
This agrees with what is mentioned in the Gospel of Matthew, "The kingdom of God shall be taken from you, and given to a nation bringing forth the fruits thereof."
C. Allah's Messenger (pbuh) said:
The likeness of the Muslims, the Jews, and the Christians is like that of a man who hired a people to do some work for him into the night, for a fixed sum, so he worked for half the day and said, "We have no need of your payment that you agreed to, and the work we have done is in vain." So he said to him, "Do not do that. Finish your work and receive your payment in full." But they refused and left. So he hired others after them and said, "Finish the rest of this day of yours, and you will have what I agreed to pay them." So they worked until the afternoon and said, "To you the work we have done is in vain, so keep the payment we have worked for." So he said to them, "Finish the rest of your work, for there is very little left of the day." So he hired others to work for him the rest of the day. They worked the rest of the day until the setting of the sun, and they received the payment of both other groups. This is their likeness and what they accepted of this light.
What Allah's Messenger (pbuh) said agrees with what it says in the Gospel of Matthew, "…and given to a nation bringing forth the fruits thereof."
D.After the Prophet Muhammad (pbuh) came and his companions (may Allah be pleased with them) believed, they began to fight battles and wars to spread true monotheism and the invitation to worship Allah (Mighty & Majestic), exclusively, without associating anything with Him and without believing anything false about Him (Noble & Sublime) or attributing to Him any impairment or shortcoming concerning His Being (Noble & Sublime), and to establish the Islamic empire.
And Allah (Mighty & Majestic) granted victory to His prophet (pbuh) and delighted him with the Islamic empire, established upon the exclusive worship of Allah (Mighty & Majestic), on noble directives, and wise and prudent standards of interaction, on the basis of goodness and virtue. Then his noble companions (may Allah be pleased with them) assumed the mission of spreading the religion of Allah (Mighty & Majestic) around the world. Only a few years had passed when countries, north and south, east and west, began to be liberated, and all who stood to stop the spread of the true religion, Islam, were broken and defeated. Both the Persian Empire and the Byzantine Empire fell into the hands of the victorious Muslims, and neither empire remained standing. This was to fulfill what was foretold in the Gospel of Matthew, "And whosoever shall fall on this stone shall be broken."
Beside what we have mentioned are many other prophecies about the Prophet Muhammad (pbuh) in the Gospels, but we shall suffice ourselves with what we have already said on the topic.