Can I submit a conference abstract that duplicates a submitted paper? I have a paper already submitted to a journal. Now, I want to try and submit an abstract to International Congress of Mathematicians 2014. The abstract basically contains the same thought and spirit of the submitted paper though I plan to rephrase it differently from the abstract and introduction of the submitted paper. Does this violate publication ethics?
If you are submitting an abstract for a contributed talk or poster at the ICM and your paper is submitted to a math journal, then there is no issue.  The mathematics community does not consider the abstract to be a publication and there is no conflict with simultaneous submission of a paper.  In fact, this would be common.

If you are writing a paper for the ICM proceedings (i.e., you are giving an invited talk), then this could theoretically be an issue.  It would be polite and proper to inquire with the journal to make sure they are OK with it, but they will certainly say yes.  ICM proceedings papers are considered expository, and being invited to speak is an honor, so there's no way anybody will interfere with it.