"I am constitutionally the president, democratically elected for five years," he said late on Friday.
"I will act. I want to work with people in the country just as much as with foreign partners who support democracy."
Besides journalists, politicians who have formed an anti-coup coalition, travelled to Lemden to meet Abdallahi, the country's first democratically elected leader.
"We should be meeting next week to discuss the strategy to adopt," the ousted president said, without giving details of his plans.
The European Union has threatened to impose sanctions against Mauritania if constitutional rule under Abdallahi was not restored.
Diplomats said the junta's transfer of Abdallahi to Lemden from Nouakchott fell far short of international demands to restore democratic government.
Abdallahi said his months of house arrest passed without discomfort.
"I was able to read books and listen to the news. I was not badly treated," he said.