Blasts have been reported in Kabul as Afghanistan’s two leading presidential candidates held separate swearing-in ceremonies after both claimed to have won last year’s elections.

The incumbent Ashraf Ghani took his oath of office at the country’s presidential palace in Kabul in a ceremony on Monday attended by foreign diplomats including the US special envoy Zalmay Khalilzad.

At about the same time, Ghani’s rival Abdullah Abdullah was holding his own inauguration ceremony despite negotiations late into the night on Sunday in an attempt to find a compromise between the rivals. Television stations in the country broadcast the two ceremonies side by side.

A spokesman for the president’s office said nobody was hurt in the explosions on Monday. It was not immediately clear where they had taken place. Islamic State claimed responsibility.

As the blasts were heard during Ghani’s ceremony, he opened his jacket and showed his shirt to the crowd. “This is not a shield, it’s just clothes,” he said. “This is sacrificed to the Afghan people. The head [of the country] is ready to sacrifice for Afghanistan.”

Fears of Taliban attacks, as well as widespread disillusionment contributed to a record-low turnout of Afghans for the elections on 28 September, with Ghani, 70, declared the winner with 50.62% of the vote in February.

But amid a voting process marred by incomplete voter lists, issues with a biometric identification system aimed at curbing fraud and reports of hostile election workers, Abdullah rejected the result and said he would form his own government.

Abdullah, 59, said during his ceremony that if he accepted Ghani’s purported victory it would “be the end of democracy in Afghanistan” and called for renewed talks to break the impasse.

Kai Eide, a former UN special representative in the country, tweeted: “Terribly sad and dangerous. Two parallel ceremonies. This simply cannot continue. Strong unity is required, not destructive rivalries.”

Afghanistan’s election commission in February said it counted 1.82m votes and discarded nearly 1m. There are about 9.6 million registered voters in the country.

Abdullah Abdullah waves to supporters during his swearing-in ceremony in Kabul. Photograph: Omar Sobhani/Reuters

The dispute threatens to leave the internationally recognised Afghan government weak and divided after the signing last week of a US agreement with the Taliban that aims to facilitate the withdrawal of most foreign troops from the country.

The Kabul government was shut out of the negotiations by the Taliban, which says it will hold separate talks with its representatives. Analysts said the political dispute is likely to delay the start of the intra-Afghan talks.

Abdullah and Ghani competed against each other in presidential elections in 2014 with similar disputed results. The disagreement led to the creation of a “chief executive” position for Abdullah, an extra-constitutional advisory role aimed at warding off instability.

The Afghan media outlet TOLOnews reported on Monday that Ghani had offered Abdullah 40% of his cabinet and a role overseeing peace negotiations with the Taliban, but that the talks foundered over how much power Abdullah himself would wield.

The second contested result in the presidential polls has added to the frustrations of Afghans, already dealing with a deteriorating security situation, high unemployment and uncertainty over the country’s future.

“After signing the deal between Taliban and Americans I was so optimistic to witness peace,” said Mohammad Mohammadi, 27, a medicine student in Herat. “I haven’t lived in peace in my life but today’s events destroyed my ambitions. Two presidents at the same time is not something that I can be hopeful of my future.

“They both are fighting for their own benefits, neither of them is planning for for me and this people,” he said. “More bad days are coming. We’re all depressed by politicians.

Hamed, 30, watched the competing ceremonies on a TV in his takeaway food shop. “I didn’t vote in this election at all but I’m do worried about future,” he said. “What can I say except that they should respect the rule of law. I’m afraid about another civil war, this time between Ashraf Ghani and Abdullah.”