KABUL, Afghanistan — Afghanistan’s monthslong election dispute, which resulted in a bizarre reality of two men taking the oath of office as president, reached a resolution on Sunday when President Ashraf Ghani gave his chief rival, Abdullah Abdullah, the leading role in the country’s peace process with the Taliban and a 50 percent share in the cabinet.

       The deal, which the Afghan presidential palace said was signed in the afternoon, draws to a close a political crisis that cast a major shadow over efforts to end the long war with the Taliban. It had complicated Afghan negotiations with the insurgents after the United States agreed with the Taliban to begin a phased troop withdrawal.

       All but one of Afghanistan’s presidential elections since the 2001 American invasion have ended in dispute, the most recent two bringing the country to the verge of more bloodshed in the middle of a raging war with the Taliban. In 2014, Secretary of State John Kerry negotiated a power-sharing arrangement that kept Mr. Ghani as president and Mr. Abdullah as the government’s chief executive with 50 percent of the power.

       After Mr. Abdullah disputed Mr. Ghani’s victory for a second term in last September’s elections, both sides dug in. They refused to come together in one government even after the United States chided both leaders and cut $1 billion in aid.

       As international pressure grew and the Taliban appeared to be benefiting from the political disarray, the two sides began talks for a way out.

       The new deal, whose negotiations were mediated by political leaders including former President Hamid Karzai, strips Mr. Abdullah of an executive role in the government but gives his coalition half the cabinet appointments. In return, Mr. Abdullah takes charge of the peace efforts with the Taliban in a new role as chairman of the High Council for National Reconciliation.

       Mr. Ghani also agreed to the formation of a High Council of Governance, which will give the country’s major political leaders an advisory role to the president in hopes of shaping a united front as Afghanistan seeks an endgame with the Taliban. Mr. Ghani struggled to create political consensus in his first five years in office, alienating many influential political figures.

       The deal also promotes Gen. Abdul Rashid Dostum, a controversial former vice president to Mr. Ghani and current backer of Mr. Abdullah, to the highest military rank, marshal.

       A strongman championing the cause of Afghanistan’s ethnic Uzbek minority through four decades of wars and politics, General Dostum has an open court case against him. The case centers on accusations made in 2016 by a political rival who said the vice president had abducted him from a crowded sports arena, tortured him and ordered his rape.