In a decision that could have far-reaching effects on immigration cases involving same-sex couples, federal officials have canceled the deportation of a Venezuelan man in New Jersey who is married to an American man, the couple’s lawyer said Wednesday.

The announcement comes as immigration officials put into effect new, more flexible guidelines governing the deferral and cancellation of deportations, particularly for immigrants with no serious criminal records.

Immigration lawyers and gay rights advocates said the decision represented a significant shift in policy and could open the door to the cancellation of deportations for other immigrants in same-sex marriages.

“This action shows that the government has not only the power but the inclination to do the right thing when it comes to protecting certain vulnerable populations from deportation,” said the couple’s lawyer, Lavi Soloway.