Gillani, who heads the new ruling coalition formed by the Pakistan People's Party and PML-N, also said he did not believe that Musharraf had any intention of using the President's controversial powers to dissolve the parliament and dismiss the prime minister.
"He (Musharraf) has been President for eight years. He has willingly doffed his uniform. And he has recently conducted an election, one that has brought pro-democracy forces into power. I don't think we will have any problem from him," Gillani said in an interview with the Nawa-i-Waqt Urdu media group.
He was replying to a question on the possibility of Musharraf using his powers under the controversial Article 58(2b) of the constitution to dissolve Parliament in case the judges deposed during last year's emergency are reinstated.
"We don't believe the President has any intention of using the clause," Gillani said. "The people gave us their mandate for the restoration of the constitution. We will have to respect that. And so does the President."
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While the PPP has indicated that it is willing to forge a working relationship with Musharraf, PML-N chief Nawaz Sharif has been insisting that the President should quit.
Gillani avoided giving a direct reply to a question on the possibility of PPP co-chairman Asif Ali Zardari becoming Prime Minister after contesting by-elections in June.
"Zardari has every right to contest the election. As far as my office is concerned, I was made Prime Minister by my party. And I will stay with the party," he said.
Referring to the peace negotiations with militant groups in Pakistan's tribal areas bordering Afghanistan, Gillani said: "Our government has a three-pronged strategy for the tribal areas