Is there any way to search a conservative sequence(consensus sequence) of a different organism or same organism with different species?
This is a rather open ended question. Do you have specific sequences/length in mind or not. There are already databases like CDD at NCBI or other databases of non-coding conserved sequences. Homologene database at NCBI is focused on conservation of gene sequences across species.
If you think about your question you'll realize that it is lacking specificity.
In general for the same organism, the entire sequence is conserved, after all it is the identical organism. A variant between the two sequences of the same organism, however large, should not be indicative of "lack of conservation". One of the variants or both may be conserved long term.
To find potentially conserved regions across organisms you can blast with your query and you'll be immediately be presented with all the regions in the other organisms that show high similarity.