Is there a PSI-BLAST for nucleotide sequences?
If you have a non-coding gene sequence (e.g. regulatory sequence) this answer should hold your solution:

Background theory


Firstly you must realize that PSI-BLAST is built for detecting "romote homologues",  (i.e. those that have a very "distant evolutionary relationship" to your query) - from a database of sequences. It is therefore known to be a "sensitive" analysis which can recruit distantly related matches but has a small chance of recruiting some false matches - "rogue homologues".
Secondly PSI-BLAST is known as a "profile method" that is it uses multiple sequences that are cumulatively recruited with each "psi-blast iteration", to build an empirical profile of amino acid residues along the positions of your query. This is in the same family of analyses as "Hidden markov models" (HMMs) in that HMMs use multiple sequences to build an empirical profile that is able to recruit distant homologous, except the "profile" includes probabilistic pathways to all the recruited sequences.


My Answer

I suggest you use a software package called HMMER. Indeed this method shares critical theoretical similarity to PSI-BLAST as well as functionality in your case (searching for remote nucleotide sequence matches in a database vs. a nucleotide query), it also does not assume your sequence is protein-coding - here is the wiki description:


  HMMER is a free and commonly used software package for sequence
  analysis written by Sean Eddy.1 Its general usage is to identify
  homologous protein or nucleotide sequences. It does this by comparing
  a profile-HMM to either a single sequence or a database of sequences.


Other possible answers

If you are afraid of using HMMER, then here is a list of all alignment software tools represented in a table that allows you to focus on only those that use nucleotide sequence as input:

http://en.wikipedia.org/wiki/List_of_sequence_alignment_software