Obama administration officials unveiled rules on Wednesday that will allow many American citizens — perhaps hundreds of thousands — to avoid long separations from immediate family members who are illegal immigrants as they apply to become legal residents.

The rules, announced by Homeland Security Secretary Janet Napolitano, create a waiver that bypasses an arcane Catch-22 in immigration law. It had presented Americans with the prospect of being separated for up to a decade from immigrant spouses, children or parents who were applying for the legal documents known as green cards.

Until now, the risks for those immigrants of leaving the United States to return to their native countries to pick up their visas, even ones that were already approved, had been so great that countless families decided not to apply, adding to the numbers of immigrants living illegally in this country.

The immigration authorities will begin accepting applications for the waivers on March 3. Administration officials first announced the policy change a year ago, but they have been receiving public comments and making revisions before publishing the final rules.