A Tax Court case (PDF) tells the story of a woman who was a young girl in her home country saw atrocities committed against Catholics and saw a Catholic Church destroyed.  After living in the United States she started making donations to her home country's Catholic Church.  The donations were not made directly, but through a relative as she may have feared reprisals.  Those donations are not tax deductible according to this opinion.  However donations to US Based organizations that do work in her home country (she eventually gave to one) would be.   Donations must be given to "a corporation, trust, or community chest, fund, or foundation."  Wiring money to her relative was none of these things.  Also, even if it did, the organization did not qualify.  She also attempted to get a tax deduction for airfare to her country, which also did not work.  

It is helpful to know, for purposes of foreign religious organizations, you may not get the tax deduction.  Many people donate to causes outside the United States regardless of the tax deductibility of the donation.  It may also be possible to get a deduction if you donate to a US Organization that works in a foreign country.