RUP with agile

Just see this it explains RUP :)
http://upload.wikimedia.org/wikipedia/en/a/aa/RationalUnifiedProcess.png

Adding to what VIjay has captured....
Agile more or less focuses on JENTM approach (Just Enough Nothing Too Much) that is applicable to the incremental delivery made at the end of an iteration. 
Each iteration delivers a functioning software product(with scope, usability and features added..as the "story" goes).
Agile does not require a Use Case Story approach....which has been the hallmark of "X"UP approaches.
Its inherent that within a RUP , there is a significant investment in a slightly larger (in terms of time, effort size and complexity) to nail down a reasonably good JENTM baselines...Agile braces itself for shifting and ever-changing customer/business priority.
Whilst its a common refrain from others...that Agile needs a very mature and disciplined team at its core....Its inherent simplicity and common-sense approach makes one wonder as to why such a hullabaloo is created in the first place?
Anyways....talking about RUP and Agile is like comparing Apples and Oranges. Each of them have a preferred growth climate and a discerning audience/ customers. 
The flavor the season can vary depend on what your taste buds are clamouring for!
Let them be as they are....both are efficient...mixing up their relative strengths into a blurry blend will lead to a burnt out project within a flash.

Dinesh,
RUP is a framework which has only one flavour while agile has many flavours like ASD (Adaptive Software Development), DSDM (Dynamic System Development Methods (DSDM), SCRUM, FDD (feature Driven Development etc.
Though both Agile and RUP are iterative in nature, Agile focuses on Continuous Integration, Re-factoring, Collective Ownership, Small Realises based on strong coding standards.
It would be difficult to merge Agile with RUP cause, Agile usually has a strong SME focus in most of the aspects and is used when the time to market and quality – both are important, also Agile uses a lot of technology in terms of automation of common processes to a very large extent. This combination is very costly to most organizations, though time to market is shorter. Also in most cases Agile has a shorter life cycle when compared to most other SDLC. 
I am sure you are aware of the other aspects of Agile which complicate things unless there is a good understanding team in place. 
The merger of Agile into RUP I therefore feel could be quite expensive and difficult to maintain. 
I would instead recommend that all such methods and models be identified in its original flavours and be utilized in accordance to the model guidance and when the nature of business requires it. Else it could be a royal mismatch.