Only US citizens can petition for parents, not permanent residents.
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I agree with my colleagues, only a USC can petition for a parent. However, if you are the spouse of a USC, you may qualify for citizenship after three years (rather than five) of obtaining your CR status.
Unfortunately not yet. You need to naturalize and become a US citizen BUT then its a fast track application since now they are in a preferred class called"immediate relatives" and then you can sponsor them without delay for green cards.
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No. Please do not forget that a conditional LPR must solicit within 90 before the 2nd anniversary of the conditional LPR to have such condition removed. To answer directly, only a US Citizen may petition for Parents.