If you are a resident for tax purposes - you will be taxed on all worldwide income (regardless of its source).
If you are a non-resident for tax purposes - you may be taxed only on income from US sources.
Please see for reference IRS publication 519 - http://www.irs.gov/pub/irs-pdf/p519.pdf for rules to determine if you are Nonresident Alien or Resident Alien
You may not use the section 1031 if the condo is your personal property.
Let me know if you need any help.