But taking that step would also open Mr. Obama to new charges that he is abusing his authority, even as the Supreme Court considers whether to review the legality of his actions to provide work permits and protection from deportation to five million undocumented immigrants.

While some gun control advocates had hoped to see Mr. Obama announce new rules on Dec. 14, the anniversary of the 2012 school shootings in Newtown, Conn., there is virtually no chance of that happening. With White House lawyers still poring over the legal questions, officials said any announcement would be at least a month away.

Valerie Jarrett and other White House advisers have held a series of meetings in recent weeks with gun control advocates who are pushing for Mr. Obama to take strong executive action in the absence of any legislation from Congress. The president and Ms. Jarrett discussed the possibility of executive actions on guns during a meeting on Friday with Gabrielle Giffords, the former Arizona congresswoman who was shot in the head during a mass shooting in 2011, and her husband, Mark Kelly.

Mr. Kelly said a detailed definition of a gun dealer would help catch some of the improper sales that are done off the books at gun shows. He said he spoke with the president about that idea early this year. “I’m optimistic that they will do something to improve the system,” Mr. Kelly said in an interview.