The Pakistani Muslim League made the offer on Thursday in the key southern province of Sindh after a spate of attacks in the provincial capital Karachi claimed more than 50 lives.
Muslim League head Chaudhry Shujaat Hussain said the Muttahida Majlis-e-Amal (MMA), a six-party Islamic alliance, backed the proposal.
But a spokesman for the Pakistan People's Party (PPP) said its leader Benazir Bhutto - forced to remain in exile by the threat of prosecution for corruption - had rejected it.
"The military government has landed itself in a mess. The PPP will not lend its shoulder to bail them out," spokesman Farhat Allah Babar said.
After the rebuff from the PPP, the biggest party in Sindh, Hussain will be hoping the MMA can use its influence with Sunnis blamed for attacking minority Shias to persuade them to curb their activities.
Hussain told reporters the deteriorating situation in Sindh required the past bitterness to be forgotten.
"A government of national consensus should be formed which should be able to restore peace in the province. We should have it with immediate effect"
Chaudhry Shujaat Hussain,
Pakistan Muslim League chief
"A government of national consensus should be formed which should be able to restore peace in the province. We should have it with immediate effect," he said.
Karachi is Pakistan's main commercial centre and on Thursday stocks on the city's long-booming stock exchange took a rare dive of more than 3%.
This was partly due to concerns about the MMA's call for a nationwide strike on Friday to protest against the killing of a senior Sunni Muslim cleric in Karachi.
Analysts have said the government will have to act firmly and quickly to prevent more widespread violence between Sunnis, who make up about 70% of Pakistan's 97% Muslim majority population, and Shias, who make up about 20%.
While the latest violence has smacked of decades-old sectarianism, analysts say it appears Sunnis activists have been using attacks on Shias as part of a broader campaign to undermine President Pervez Musharraf and his support for the US-led "war on terror".
President Pervez Musharraf has accused al-Qaida of being behind previous attacks, including two attempts on his life in December.
A senior police investigator, Gul Hasan Sammo, said the bomber who carried out the latest attack in Karachi, which killed at least 21 Shia Muslims at a mosque on Monday, came from the outlawed Sunni group Lashkar-e-Jhangvi.
MMA leader Fazlur Rahman (C) is
set to share power in Sindh
Lashkar-e-Jhangvi is perhaps the most feared of Pakistan's underground groups and allegedly has links to Usama bin Ladin's al-Qaida network.
However, no group has claimed responsibility for the bombing.
Meanwhile, Pakistani authorities imposed a curfew on the northern city of Gilgit on Thursday to quell anger among Shia Muslims over school curricula.
Local Shias staged a protest rally in defiance of the curfew and police opened fire when the protesters attacked a police training centre and the state-run radio station.
Protesters tried to set ablaze a vehicle belonging to the radio station, residents said.
Dozens of people were arrested for violating the curfew, including eight Shia leaders, the administration said.
Shias are angry that some schools only teach methods of prayer followed by the rival Sunni majority.
At least three people were injured in an exchange of gunfire in the city's Khomer neighbourhood, residents said.