"Powers to all the institutions flow from Parliament," said Ashraf, who won a parliamentary vote to become prime minister last week.
"Parliament manifests the aspirations of the people and we shall ensure that nobody else exercises this right of Parliament and the people."
Ashraf, 62, also warned against forces trying to undermine the supremacy of Parliament and vowed to hold free and fair elections, a report by the Associated Press of Pakistan said.
But the premiership of Ashraf and his Pakistan People's Party have a rough road ahead of them before a national election is held early next year -- if his tenure can run that long.
Ashraf won 211 votes in the 342-seat Parliament, thanks to the backing of the smaller Pakistan Muslim League-Q.
Ashraf and his Cabinet likely will thank the PML-Q by giving one of its leaders the deputy prime minister position this week, a report by the news agency PakTribune said.
The new prime minister already has visited PML-Q President Chaudhry Pervaiz Elahi who said he would take disciplinary action against party members who didn't vote for Ashraf, a report by Dawn, a Pakistani newspaper, said.
Elahi also said Ashraf promised the government would make it a priority to sort out the country's energy problems, something with which Ashraf is particularly familiar.
Ashraf is in the Supreme Court fighting allegations of corruption and bribe taking relating to the Rental Power Plants scheme he introduced when he was water and power minister.
The scheme involved private companies setting up small temporary power generation plants that could run during times of peak energy consumption, a plan to avoid power shortages and outages.
But in March 2011, the Supreme Court declared the Rental Power Plants scheme illegal and all RPPs were ordered to shut down immediately.
Ashraf's alleged involvement in the case is one reason he was shuffled out of the portfolio and into the Ministry of Information and Technology, the report by PakTribune said.
The new prime minister's relationship with the Supreme Court could become more intense if he has to field calls from judges that the government launch a corruption investigation against President Asif Ali Zardari, a report by the BBC said.
It was the refusal by Ashraf's predecessor, Syed Yousuf Raza Gilani, to launch such an investigation that led to his conviction for contempt of court in April and his eventual disqualification from public office earlier this month.
It was the political demise of Gilani, 60, that paved the way for last week's parliamentary vote.
Gilani had argued that Zardari, who is also co-chairman of the PPP, has immunity from prosecution.
Zardari, 56, and his late wife Benazir Bhutto -- a former prime minister -- are accused of using Swiss bank accounts to launder bribe money, the BBC said.
Pakistan can't afford a lame-duck government at this time, noted the BBC report.
The country's economy is in crisis, relations with the United States are at low ebb and militants continue to wage a violent campaign in tribal areas near the Afghan border.
"We want peaceful ties with our neighbors Afghanistan, Iran and India," Ashraf said in his inaugural speech last week.
"We desire good relations in our region on the basis of the philosophy of peaceful co-existence."