"If we have actionable intelligence about high-value terrorist targets and president Musharraf won't act, we will," Obama said on Wednesday.
"I understand that President Musharraf has his own challenges, but let me make this clear: there are terrorists holed up in those mountains who murdered 3,000 Americans. They are plotting to strike again."
US sources have also spoken of concerns new recruits could be being trained there for attacks against the US.
Azeem said: "Such statements are being made out of sheer ignorance. They are not fully apprised about the ground realities and not aware of the efforts by Pakistan."
Islamabad has bristled against a string of similar threats in recent weeks by the administration of George Bush, the US president, whose top counter-terrorism official in July refused to rule out US strikes in Pakistan.
Azeem said: "We have said before that we will not allow anyone to infringe our sovereignty.
"If there is any actionable intelligence they should tell us and only our forces will take action on it and they are quite capable of it."
The minister suggested that Obama's comments were prompted by Washington's inability to curb the ongoing Taliban campaigns in neighbouring Afghanistan, where US-led forces toppled the Taliban regime in late 2001.
"This seems to be a reaction to their own failure in Afghanistan to control the US casualties and instead of addressing the situation there, they are finding scapegoats and damaging their own cause," Azeem said.
Tasnim Aslam, a spokeswoman for Pakistan's foreign ministry, told AFP she would not comment as Obama was not president, but added: "These are serious matters and should not be used for point-scoring.
"Political candidates and commentators should show responsibility."
The Illinois Democrat is trying to convince Americans he has the foreign policy heft to be president after Clinton questioned his readiness to be commander-in-chief.
Clinton last week labelled Obama naive for saying he would be willing to meet the leaders of Iran, Cuba, Syria, North Korea and Venezuela without preconditions in his first year in office.
A poll by The Wall Street Journal and NBC News said Clinton has widened her lead over Obama, going up to 43 per cent in July from 39 per cent in June.
Obama tallied 22 per cent, down from 25 per cent in June.
Those polled cited Clinton's experience and competence highest among her positive attributes.
Obama said he would make hundreds of millions of dollars in US military aid to Pakistan conditional on Pakistan making substantial progress in closing down training camps, evicting foreign fighters and preventing the Taliban from using Pakistan as a staging area for attacks on Afghanistan.
The White House said Pakistan was working hard to fight al-Qaeda and the Taliban, and Washington was doing what it could in support.
"At the same time, we recognise the sovereignty of the Pakistani government and realise that they're putting on a serious push… They're taking the fight to al-Qaeda," spokesman Tony Snow said.