President Ashraf Ghani met with his Chief of Executive Officer Abdullah Abdullah on Thursday evening to solve their disagreements, the CEO's office said.
Ghani has reportedly insisted that the national unity government (NUG) agreement must be implemented and that they should work together in the interest of the nation.
The CEO's office said that at the meeting, which was the second such get-together, Ghani shared his viewpoints about the requests presented by Abdullah and that Abdullah will soon share the president's views with his political allies.
Omid Maisam, spokesman for the CEO office said: "In this meeting Ghani insisted on the implementation of the NUG agreement, cooperation and electoral reforms. The next meeting will be an opportunity for solving the disagreements."
It is not known when the rift between Ghani and Abdullah will be resolved but civil society members warn that if these disagreements continue it would have negative consequences.
"NUG leaders should not sacrifice everything because of their disagreements anymore. These tensions have badly affected the security, economic and political situation of our country," said Sayed Nasir Mousavi, a civil society member.
However, ending the rift is critical for leaders ahead of the Brussels Summit.
"People cannot tolerate this situation anymore. They should not test peoples' patience," said Noor Ahmad Bashar, a political analyst.
At the first meeting, the CEO presented a list of suggestions to Ghani. It is hoped that they will solve their political disagreements at their third meeting.
Solving these disagreements is seen as a test for both leaders as the NUG approaches the end of its second year.