So even though the Lord Jesus told them this they were not saved when they believed?:
"Very truly I tell you, whoever hears my word and believes him who sent me has eternal life and will not be judged but has crossed over from death to life" (Jn.5:24).
Of course the Jewish believers who lived under the law were saved since they received eternal life upon belief. And those who believed will never perish, meaning that they possessed eternal security:
"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life" (Jn.3:16).
It is ridiculous to argue that the Jews who lived under the law would not be saved until sometime in the future. Here the Lord Jesus told a woman that she was already saved:
"And he said unto her, Thy sins are forgiven. And they that sat at meat with him began to say within themselves, Who is this that forgiveth sins also? And he said to the woman, Thy faith hath saved thee; go in peace" (Lk.7:48-50).
Peter also knew that he was already saved and that his salvation was on the principle of "grace":
"We believe it is through the grace of our Lord Jesus that we are saved, just as they are" (Acts 15:11).
Those who lived under the law were saved by grace through faith:
"Therefore it is of faith, that it might be by grace; to the end the promise might be sure to all the seed; not to that only which is of the law, but to that also which is of the faith of Abraham; who is the father of us all" (Ro.4:16).
Since the Jews who lived under the law were saved by grace through faith it is evident that "works" played no part in their salvation:
"Now to him that worketh is the reward not reckoned of grace, but of debt" (Ro.4:4).
Here is what the Lord Jesus Himself said about those to whom He had given eternal life:
"And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand" (Jn.10:28).