"I am pleased to assume my responsibilities (as president), I took them on for a five-year term," Wulff said in a televised interview amid a growing chorus of calls for his resignation.
He added that he hoped by the end of the term in 2015 "to have a record showing I was a good and successful president."
Wulff, 52, landed in hot water last month when the powerful daily Bild reported that he had concealed a home loan at an advantageous interest rate he accepted from the wife of a tycoon friend while premier of Lower Saxony state.
When opposition state deputies asked him whether he had business ties to the tycoon or any firms connected with him, Wulff had kept quiet.
This week it emerged that Wulff had called Bild's editor-in-chief Kai Diekmann one day before the story's publication and left a blistering voicemail message threatening him with "war" if he went ahead with the report.
Meanwhile another publication, Welt am Sonntag, said one of its reporters had been summoned to the presidential palace for a dressing-down over another article about Wulff's strained relationship with his half-sister.
Wulff said in the interview Wednesday that the call to Diekmann had been a "serious mistake" that was "unworthy" of a president and for which he had already apologised.
On the loan, Wulff insisted it had been a private arrangement with a friend rather than a business deal.
"I would not like to be president of a country in which you can no longer borrow money from a friend," he said.
Wulff said he would not resign as he had received strong support from Germans in recent weeks calling on him to stay in office.
A spokesman for Merkel, Georg Streiter, said earlier Wednesday she was sure that Wulff would offer a full explanation of the affairs, as political pressure mounted on both of them.
"The chancellor is absolutely confident that the president will continue to answer all open questions completely," Streiter told a regular government press briefing. "She has enormous respect for the work of the president."
The media uproar is an unwelcome political distraction for Merkel as she grapples with the eurozone debt crisis at the start of what is expected to be a turbulent year, and a replacement for Wulff would be tough to find.