"In my view, the situation is improving, the democratic process is continuing and terrorism has been controlled," he said.
Kamal Hyder, Al Jazeera's correspondent in Islamabad, said: "What you saw today was a very different Musharraf - a political Musharraf rather than a military Musharraf.
"He extended an olive branch to Nawaz Sharif and Benazir Bhutto, and he said that a level playing field was provided [for elections on January 8].
"The emergency lifting was a great demand of the international community, and of civil society and politicians in Pakistan.
"Hopefully, such language from the president would indeed be bringing rays of hope as far as Pakistan's troubled political situation is concerned," Hyder said.
Musharraf was sworn in as a civilian president in Islamabad, the country's capital, earlier in the day.
The oath was taken at the Aiwan-e-Sadr presidential palace one day after Musharraf stepped down as the head of Pakistan's military.
Wearing a dark traditional tunic, he pledged to uphold the constitution and to do his utmost to preserve and protect the nation.
Abdul Hameed Dogar, the chief justice Musharraf hand-picked after purging the supreme court when he imposed emergency rule on November 3, administered the oath to Musharraf.
Musharraf said: "We want democracy, we want human rights, we want stability, but we will do it our way," in his first speech as civilian president.
"We understand our society, our environment, better than anyone in the West," he said.
Musharraf welcomed the return from exile of Benazir Bhutto and Nawaz Sharif, both former prime ministers at the swearing-in ceremony.
He said: "Benazir Bhutto and Nawaz Sharif are back. I personally feel this is good for the political reconciliation I have spoken of."
However, neither were present at the ceremony and it remains unclear whether the changeover will defuse the threat of a boycott of the elections.
Such a move would undercut Musharraf's effort to legitimise his rule through a democratic ballot.
As civilian president, Musharraf will have the power to dismiss the government.
On Wednesday, however, Bhutto said that she was "not in a hurry to accept Pervez Musharraf as a civilian president".
Hyder said: "After the president's speech tonight, they [opposition members] will be thinking vey seriously about bringing the country towards reconciliation, or confrontation."
Meanwhile, Sharif has said that Musharraf's oath of office had no legitimacy and he demanded the reinstatement of judges sacked under the emergency.
In the city of Lahore, about 250 lawyers in black suits clashed with police outside the city's main court.
"We don't accept Musharraf even without his uniform. He has to go," said Malik Mohammad Arshad, a lawyer.