Addressing the first meeting of his cabinet since assuming office last week, Ashraf said Pakistan values its relations with Islamic world, the US and China as well as neighbours like India and Afghanistan.
He listed a crippling energy crisis and criticism of governance as other challenges facing the Pakistan People's Party-led government.
"My government is mindful of the fact that extremism, militancy, intolerance, sectarian violence and terrorism, all put together, have posed a serious challenge to our sovereignty, security and national cohesion," he said in his opening remarks at the meeting.
"We as a nation have to thwart the sinister designs of these forces and the government, on its part, will work with lot of dedication to establish the writ of the state, wherever they operate".
The premier said Pakistan will not allow its "land to be used against any country for any terrorist activity".
At the same time, its expects its "neighbours and other powers to refrain from interfering in the internal affairs of Pakistan", he said.
Ashraf, who last week replaced Yousuf Raza Gilani after he was disqualified by the Supreme Court, acknowledged that Pakistan-US relations were "passing through a very delicate and critical phase" and said Islamabad would not make "hasty and emotional decisions that do not auger well".
Ashraf pointed out that NATO supply routes to Afghanistan were "blocked because of an unprovoked attack" on a Pakistani check post last year.
"The unconditional apology from the US for this blatant attack is the demand of the Parliament and we shall proceed always keeping our national interests in view," he said.
Pakistan has been unable to make a breakthrough in protracted talks with the US to end the six-month blockade of the NATO supply lines due to Islamabad's insistence on an apology and differences between the two sides on the fees to be paid for supplies transported through Pakistani territory.
Ashraf, 61, has been thrust into the position of the premier at a time when the PPP-led government is grappling with several challenges, including an economic downturn, power outages that have triggered violent protests in the most populous province of Punjab and a confrontation with the Supreme Court.
Referring to these challenges, Ashraf said the PPP "strongly believes that politics of confrontation should be shunned, for which all democratic forces need to show sincerity of purpose, prudence and maturity, allowing space to their opponents".
"You all are aware that we face challenges, which are very serious in nature and if not addressed effectively and properly, could even shake the foundations of democracy.
"In order to sustain and strengthen democracy, this Cabinet will have to grapple with the issues and problems with zeal and dynamism," he said.
The people had been disheartened by "negative propaganda" and "confusion" and the government has "to do something special to pull the nation out of dejection and galvanize them into activity and forward movement", Ashraf said.
Ashraf said his cabinet will "work in continuation of the policy already in place" but make necessary adjustments as warranted by the changing situation.