You would use a colon or semi-colon when joining 2 independent clauses. But in your example, the second clause

as necessity of additional time for rectifying the algorithms, lengthy literature survey than expected and etc.

refers to "reasons for my extension request" in the first clause. Also the first clause is not independent (able to stand by itself). So you should use a comma instead.

Here, I would like to summarize the reasons for my extension request, due to the necessity of additional time for rectifying the algorithms, lengthy literature survey than expected and etc.

I used due to because the second clause is explaining or expanding on the first clause.

You would use a colon or semi-colon when joining 2 independent clauses. But in your example, the second clause

as necessity of additional time for rectifying the algorithms, lengthy literature survey than expected and etc.

refers to the reasons for summarizing mentioned in the first clause. Also the first clause is not independent (able to stand by itself). So you should use a comma instead.

Here, I would like to summarize the reasons for my extension request, due to the necessity of additional time for rectifying the algorithms, lengthy literature survey than expected and etc.

I used due to because the second clause is explaining or expanding on the first clause.