Updated

The Obama administration confirmed that gay citizens can apply for a visa for a foreign spouse now that the Supreme Court has struck down part of the Defense of Marriage Act that limited such privileges to heterosexual couples.

Homeland Security Secretary Janet Napolitano said Monday that same-sex visa petitions must be processed “in the same manner” as those filed by opposite-sex couples, one day after a lawyer for an American man and his Bulgarian male spouse said his clients became the first gay couple in the United States to have their application approved.

Even gay couples living in states that don’t recognize same-sex marriages can apply for the visa as long as they were married in a state (or foreign country) that recognizes such marriages.

The first gay couple that purportedly had their visa application approved, for example, was married in New York but they live in Florida, which does not recognize same-sex marriages.

Napolitano issued the statement a few days after President Obama said the high court’s ruling means the federal government must respond “swiftly and smoothly” in implementing benefits for such couples.

The decision Wednesday gives married gay couples access to most the federal benefits that married heterosexual couples have.

“To that end, effective immediately, I have directed U.S. Citizenship and Immigration Services to review immigration visa petitions filed on behalf of a same-sex spouse in the same manner as those filed on behalf of an opposite-sex spouse,” Napolitano said on Monday in a statement.

Napolitano hinted hours after the high court’s 5-4 decision that immigration law would change.

"Working with our federal partners, including the Department of Justice, we will implement today's decision so that all married couples will be treated equally and fairly in the administration of our immigration laws," she said.

The agency did not respond Tuesday to questions about many same-sex visa applications the government expects. However, most estimates are in the range of tens of thousands, with the group Immigration Equality putting the number at about 36,000.

Those who receive a visa will be able to apply for a green card, which gives a spouse permanent resident status and a pathway to citizenship.

Vermont Democratic Sen. Patrick Leahy tried to insert such an amendment into the chamber’s recently passed immigration legislation but was stopped by party leaders who feared losing much-needed conservative votes and knew the Supreme Court would instead address the issue.