Yes, He did!
Many, including many anti-missionaries will say that Jesus (Y'shua) never said He was the Messiah and they use that claim in their many and falacious arguments that he was not the long-awaited Messiah. Why it is so hard for so many to believe that Y'shua was the Messiah is very hard for me to comprehend. He taught nothing but the Word of YHWH, and He did what He said He came for: to preach the Kingdom of Elohim. (Luke 4:43).
But for a man to say He was the Messiah in the early 1st Century CE is exactly like a Jew (or even a Christian) today in ISIS-held part of Iraq. If a Jew were to stand up today in a crowd of ISIS or ISIS supporters, it would mean certain death! Yet for some reason, the conditions at the time of Y'shua's ministry are not considered. The anti-missionaries and Messiah-deniers like to say: "He never said he was the Messiah!" as part of their unjustified reason not to believe in Him.
The problem is, He did say He was the Messiah!
Turn to Mark, Chapter 14. (I am using the AENT). Y'shua had conducted Himself rather clandestinely for about 3 years, teaching the Word. His clandestine teaching was in the open, yet not overt, for the very reason mentioned above! Yet His reputation was now "out" and He was betrayed and arrested. In Mark 14, verse 53 we find: "Then they took Y’shua to Qayapa the high priest and the chief priests and scribes and elders were all were gathered with him." In verses 60-61 we read: "And the high priest arose in the midst and questioned Y’shua and said, 'Why do you not answer the accusation they are testifying these things against you?' But he was silent and did not answer him anything. And again the high priest asked him and said, 'Are you the Mashiyach, the Son of the Blessed One?'"
Pay close attention to Y'shua's response, verse 62: "I am. And you will see the Son of man sitting at the right hand of power and coming upon the clouds of heaven."
"I AM", He said! That statement valid in any court of law, even today! And take a look at this::
In Matthew 16:15-17, He
acknowledged the question: " 'But you,' he said to them, 'who do you
say I am?' Shim`on Kefa answered, 'You are the Mashiach, the Son of the
living God.' 'Shim`on Bar-Yochanan,' Yeshua said to him, 'how blessed
you are! For no human being revealed this to you, no, it was my Father
in heaven.' "
In John 4:19-26 A woman addresses Him saying she knew the Messiah was coming and Jesus responded, "I am he."
John 10, a whole angry mob was wanting to stone him and in verses 34-36
He he explains and concludes "then are you telling the one whom the
Father set apart as holy and sent into the world, 'You are committing
blasphemy,' just because I said, 'I am a son of Elohim'?"
Y'shua is the Messiah, and He said so! But the Jewish leadership refused to believe it, and handed Him over to Peelatos. You know the rest of the story if you bothered to read it. Peelatos, the prefect of the Roman province of Judaea at the time, found no fault in Y'shua (John 19:6). But the Jewish leadership, threatened so by Him, had Him executed.
I find it ironic, that still today, 2000 years later, most of Jewish leadership still continues to execute Him.