Though the case is being treated as an anomaly that breached accepted procedures, a senior agency official acknowledged that there were no written guidelines on the handling of such letters, and that there was no way to know whether similar correspondence had prompted arrests and deportations.

If the investigation bears out what officials have learned so far, “it also flies in the face of our stated priorities to target criminal fugitives,” said the official, who spoke on the condition of anonymity because the agency had not authorized further discussion of the case.

So far, it appears that Ms. Jamieson’s Jan. 10 letter to the president reached the executive secretariat of the immigration enforcement agency on March 8. The secretariat, which handles all official correspondence, sent it to the New York field office the next day, asking for help in drafting a response.

The letter explained that Ms. Jamieson, 42, had filed a petition seeking a green card for her husband on the basis of their 2005 marriage. But before they met, Mr. Takoulo, who first arrived in the country on a temporary business visa, had applied for political asylum and had been denied it by an immigration judge in Baltimore, who ordered him deported.

Only if the agency’s chief counsel in Baltimore agreed to reopen the case, the letter said, could that order be suspended long enough for the couple to safely go to federal immigration headquarters in Manhattan for an interview to prove that their marriage was not a sham.

Mr. Takoulo, who had helped write the letter, recalled how he had imagined the president would react. “My hope was that he would call the chief counsel and say, ‘This is ridiculous  just open this case,’ ” Mr. Takoulo said, adding: “He’s even said on TV that he needs engineers.”