Prime Minister Yousuf Raza Gilani told reporters that Washington should not discriminate between South Asia's two nuclear armed nations.
Pakistan has long opposed efforts by the US administration to push through the deal with India.
Critics warned that approving it could lead to a regional nuclear arms race.
The US deal with India, which was approved by the US on Thursday, allows Delhi access to US civilian nuclear technology and fuel in return for inspections of its civilian, but not military, nuclear facilities.
Nuclear threat
“Now Pakistan also has the right to demand a civilian nuclear agreement with America,” Mr Gilani said.
“We want there to be no discrimination. Pakistan will also strive for a nuclear deal and we think they will have to accommodate us.”
Pakistan developed its atomic weapons programme to counter the alleged nuclear threat from India, its regional rival.
The BBC's Barbara Plett in Islamabad says Pakistan has been very concerned by US support for India's civilian nuclear programme.
Now that the deal has been passed, Mr Gilani told reporters that Pakistan would be justified to ask for a similar agreement.
However, Washington has already indicated that Pakistan's track record of nuclear proliferation disqualifies it from such an arrangement.
In 2004, the top Pakistani nuclear scientist AQ Khan admitted to passing on nuclear secrets to Libya, Iran and North Korea. He retracted his confession in 2008.
Newspaper reports have suggested that Pakistan's leaders might now turn to China for help with civilian nuclear technology.
Pakistan became a nuclear power in 1998 after testing devices in response to underground tests done by India.