U.S. special envoy Zalmay Khalilzad and Afghan President Ashraf Ghani on Wednesday discussed a U.S. deal with Taliban militants on a week-long reduction in violence, meeting the day after Ghani was declared a winner of a disputed presidential poll.

Ghani's main rival, Abdullah Abdullah, who came in second, rejected the result and vowed to form his own government, threatening new political turmoil as the United States strives to seal a U.S. troop withdrawal deal with Taliban militants.

The Afghan presidential palace in a statement quoted President Ghani as telling Khalilzad he had held "effective" meetings with local leaders on how the Afghan government would handle the peace process.

The U.S.-Taliban deal was struck in protracted negotiations in the Qatari capital Doha and was announced on Friday after a meeting between U.S. Secretary of State Mike Pompeo, Ghani and U.S. Defense Secretary Mark Esper in Munich.

Khalilzad, who has led talks with the Taliban on a U.S. troop withdrawal agreement, briefed Ghani on the steps that will be taken after the reduction in violence agreement comes into force, the presidential palace statement said.

Afghanistan's acting interior minister had said on Tuesday that the accord would come into force in the next five days, even as clashes between the Taliban and Afghan security forces continued.

The statement following the Khalilzad-Ghani meeting did not mention the Afghan president's re-election, which is being disputed by a number of Ghani's political opponents. The United States has not yet formally congratulated Ghani on his re-election for five more years as president.

Five years ago, in the wake of allegations of widespread fraud and corruption in the presidential election, the U.S. broke a power-sharing deal as a so-called "unity government," in which Abdullah was offered the post as chief executive.

The United Nations on Wednesday said it would "encourage the electoral management bodies to address the candidates' understandable desire to have clarity on decisions taken related to audits and recounts."

The European Union said it considered the election process to have reached a conclusion. On Wednesday, Josep Borrell Fontelles, high representative of the European Union, called Ghani, allegedly congratulating him on winning the elections.

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(With input from Reuters)