Ambassador Munir Akram complained that Ban Ki-moon was meddling in Pakistan’s affairs by saying the country should return to democratic rule.
But after meeting Mr Akram, Mr Ban repeated his concerns.
He joined Pakistan ex-PM Benazir Bhutto in saying Gen Musharraf should resign as army chief and hold elections.
Ms Bhutto, who has been negotiating a power-sharing deal with the president, said on Tuesday that she had no plans to meet Gen Musharraf.
She is currently in Islamabad to discuss the crisis with other opposition leaders.
Mr Ban relayed to reporters what he had told Mr Akram at their meeting on Tuesday.
“I again expressed my deep concern and regret [at] what had happened in Pakistan.
We think it’s an internal matter and the United Nations has no business to pronounce itself on that
“I also urged strongly that the Pakistani government should return to democratic rule and procedures as soon as possible,” Mr Ban said.
He called for the release of political leaders and lawyers detained during the crisis in Pakistan and for restrictions on the media to be removed.
But Mr Akram told the BBC that Pakistan’s emergency did not have implications for international peace and security and was therefore outside the UN’s remit.
Violent clashes between police and lawyers have continued in Pakistan
“We think it’s an internal matter and the United Nations has no business to pronounce itself on that,” he said.
The UN Security Council, meanwhile, has been silent on Pakistan, in contrast to the stance it has taken recently over Burma, says the BBC’s Laura Trevelyan at the UN.
The Security Council’s mission is to deal with threats to international peace and security.
But Pakistan is seen as a country where the US has influence and is actively applying pressure, our correspondent says.
Diplomats say it is not clear what the Security Council could do.
President Musharraf imposed emergency rule on Saturday.
The Pakistani mission to the UN said Mr Akram had explained to Mr Ban “the grave and multiple challenges which had compelled the government of Pakistan to declare the emergency”.
It said the emergency measures were “restricted” in scope.
“Governance continues as close as possible to the constitution with the cabinet, assemblies, governors and other organs of the state functioning normally,” the mission said in a statement.
“Pakistan remains committed to restore normalcy, rule of law and democracy.”
The Pakistani government’s crackdown on pro-democracy activists continued on Tuesday with dozens of arrests reported.
The country’s sacked chief justice, Iftikhar Chaudhry, called for his countrymen to “rise up” and restore the constitution.