ANSWER: The New Testament cannot give us a direct meaning of the abbreviation INRI because it is not found in the New Testament. These letters represent Latin words. The New Testament was originally written in Greek.
A little background, however, will prove helpful before answering the question regarding the meaning of INRI. In 30 A.D., when Jesus died on the cross, the Roman Empire had used crucifixion for at least 100 years (they crucified 6,000 slaves in 71 B.C. who had followed ex-gladiator Spartacus' rebellion).
The Romans, who were many times known for their brutality, performed crucifixions as a public warning to dissuade others from violating its laws. As a convicted person was escorted to the place of their execution, it was common for a Roman guard to carry a sign stating the official crime they were charged with. Pontius Pilate, the Roman Prefect over Judea from 26 to 36 A.D., used the charge the Jewish authorities gave him as the written reason why Christ was condemned.
Three different charges
What few people realize is that the charges against Christ, which were meant to justify his arrest and receiving the death penalty, were changed THREE times! The initial charge, brought against him by two false witnesses, was that he threatened to destroy Jerusalem's temple and rebuild it in three days (Matthew 26:59 - 61). This was changed to blasphemy when Jesus, under oath from the High Priest, stated he was God and the Messiah of mankind (verses 62 - 66). Although the religious leaders, in front of whom he testified, decided Jesus deserved death, they did not have the authority to carry out capital punishment. In order to have him executed by the Roman Empire, the Jews changed AGAIN the charge against him to the Roman crime of TREASON (John 18:29 - 35, 19:12, Luke 23:1 - 3)!
A capital crime
The book of Matthew gives us an idea of what was placed over Jesus' head when they hung him on the cross. What Pilate wrote was "This is Jesus, the King of the Jews" (Matthew 27:37, HBFV throughout).
The book of Mark (Mark 15:26) and Luke (Luke 23:38) has similar wording. Interestingly, while the references in Matthew and Mark do not tell us which languages the accusation was written in, Luke and John DO tell us what languages they were.
19. And Pilate also wrote a title and put it on the cross; and it was written, "Jesus the Nazarean, the King of the Jews." . . . it was written in Hebrew, in Greek and in Latin (John 19:19 - 20, see also Luke 23:38)
One reason why the abbreviation INRI is used to represent the charge against Christ is that scholars generally used the wording presented in the Gospel of John as opposed to Matthew, Luke or Mark. They did this because they felt the reference to Christ's hometown of Nazareth was a more complete and accurate recording of the charge against him than the other three gospel accounts.
Additionally, although the New Testament was written in Greek, the Latin version of John's recorded accusation was used (in pictures of the cross, etc.) due to an early translation of the Scriptures. In the late fourth century A.D., Jerome translated the original language text of the Bible to Latin, creating the Vulgate (Latin) translation. It became such an important translation, especially for the Catholic Church, that in the 16th century they made it their "official" Bible. As a side note, Latin was not only the official language of the Roman Empire but also the Catholic Church.
The abbreviation INRI
Here, then, is a breakdown of what each of the Latin letters in the abbreviation INRI mean. The letter "I" represents Jesus' name spelled Iesus. Strangely, even though Latin has a letter "J" in their alphabet, it was decided to spell Christ's name beginning with an "I." This is probably because Greek and Hebrew do not have a letter "J" in their alphabets. The letter "N" stands for Nazarenvs, which in English is Nazareth or Nazarene, the place where Christ grew up.
The letter "R" stands for Rex, which translated is "king." The last letter 'I' is an abbreviation for the word Ivdaeorum, which translated is "Jews" (again, using "I" in place of using of "J"). In English, the meaning of INRI literally is "Jesus Nazareth King Jews."