The electoral commission says incumbent Ashraf Ghani narrowly won September's vote, but Abdullah Abdullah alleges the result is fraudulent.

The old rivals both held positions in the previous government.

It comes as Afghanistan prepares to enter peace talks with the Taliban, hoping to end years of violence.

Experts have warned the current political rivalry will "gravely affect the government's position in the upcoming intra-Afghan talks".

"Unity is the only way [forward] if they want to win on the negotiating table," political analyst Atta Noori told news agency AFP.

Mr Ghani, who has been president since 2014, held his inauguration ceremony at the Presidential Palace. Mr Abdullah held his at the Sapedar Palace - despite his team earlier saying they would be prepared to cancel it, following the intervention of US Special Envoy Zalmay Khalilzad.

Mr Khalilzad is trying to work out a power-sharing arrangement between the two camps, with people on the ground clear-eyed about what two rival administrations would mean for Afghanistan.

"It's impossible to have two presidents in one country," one Afghan man told AFP. "Instead of [both] holding oath-taking ceremonies they should talk to each other to find a solution."

The political showdown comes days after Mr Abdullah escaped unharmed from an attack claimed by Islamic State militants, which saw at least 32 people killed.

It was the first major attack in the capital since the US and Taliban signed a deal in late February, which required the Taliban will hold talks with the Afghan government.