According to the statement issued by Abdullah's office, the meeting took place on Monday, reports TOLO News.
Rouhani said that he hoped the peace efforts will work in Afghanistan's favour and insisted on the implementation of joint economic plans between the two countries, the statement said.
On his part, Abdullah spoke of recent developments in the peace efforts, the ongoing negotiations in Doha, and stressed Afghanistan's will to achieve permanent peace with dignity.
He appreciated the "principled" stance of Iran in supporting the Afghan peace efforts and called for the continuation of support, the statement said.
Abdullah further he supports the effort to implement economic plans for the two countries and said that doing such could provide the foundation for peace and further regional cooperation.
The top Afghan official reached Iran on Sunday on a two-day visit, reports TOLO News.
His trip came amid ongoing peace negotiations between delegates from the Islamic Republic of Afghanistan and the Taliban.
The peace negotiation officially started on September 12. But direct talks are yet to begin due to disagreements on procedural rules.
Before this trip, Abdullah had also visited Pakistan and India where he discussed the Afghan peace process.
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