I want to rephrase and reproduce some part of the Introduction of a Research publication without giving citation to that publication. Will it be considered an act of plagiarism ?? I am not using and citing any result or any table and figure of the publication.
Unequivocally, yes. Plagiarism isn't limited to results or figures alone. As for automatic plagiarism-checkers, they will make even less of a distinction, and will almost certainly flag it as plagiarised if a certain contiguous amount (I am told it is 2 sentences, but I don't have a confirmation on this).
You mentioned rephrasing - this could help avoid automated checks, but if the changes are trivial (changing voice, shifting subject/object, substituting synonyms), a reader may spot and report this.
That aside, why would you want to reproduce it? Different papers should have different introductions if their motivations are different. Is it to save writing time/effort or something else?
I don't think it takes you anything to cite this reference. Please do cite, otherwise, if you don't like the reference, get a different reference with similar information and cite it.
If someone queries or asks you about that information, how do you attribute it to the original author?
For many of the things we write, among other reasons, we cite to show who