Former Prime Minster Nawaz Sharif, who heads the junior partner in the coalition, demanded Saturday that the dominant Pakistan People's Party agree to slash the president's powers before he would support its candidate.
Asif Ali Zardari, head of the PPP and widower of the party's assassinated leader Benazir Bhutto,.
Sharif also pushed forward the deadline for the restoration of dozens of judges dismissed by Musharraf - another key issue dividing the two main parties since they forced the president from power less than a week ago.
Still pressure was building for the two sides to end differences that appeared increasingly irreconcilable.
Presidential elections by parliament were set for Sept. 6 and the political infighting is a distraction from militant violence flaring in the volatile northwest, where 37 insurgents were killed Saturday in retaliation for a string of deadly suicide bombings.
Though Zardari is a longtime Musharraf critic, he would likely continue the former general's support for the U.S.-led war against terrorism.
But Zardari's climb to power would dismay many in this nation of 160 million who view him as a symbol of corruption that tainted its last experiment with civilian rule in the 1990s. He won the nickname "Mr. 10 Percent" for alleged graft during his wife's turns as prime minister.
Despite the backing of the PPP, Zardari's election is far from certain.
Sharif, who heads the second-largest party in parliament, was one of Bhutto's bitter rivals and has been threatening to bolt in the struggle over power.
He demanded after meeting with Zardiri's lieutenants Saturday that the PPP agree to sharply reduce the powers of the new president before he would support their candidate.
Sharif, ousted by Musharraf during his 1999 coup, wants the head of state to be deprived of the constitutional right to dissolve parliament or to appoint chiefs of the armed forces - but Zardari's name was thrown into the race without any such guarantee.
Sharif, also pushed up a middle-of-the week deadline for the restoration of judges fired by Musharraf late last year to avoid challenges to the former strongman's rule.
He wants an agreement by Monday that all the judges - including former Chief Justice Iftikhar Mohammed Chaudhry - will be back on the bench, saying a surprise Sept. 6 presidential election date forced him to push up his deadline.
Although Zardari wants the judges reinstated, he is not quite as enthusiastic. Like Musharraf, he has accused Chaudhry of being too political, and says it should be up to parliament to decide.
Analysts say Zardari also might fear that the former chief justice would revive corruption cases killed off by Musharraf as part of a failed effort to form a pro-Western power-sharing deal with Bhutto before her assassination.