A four-member delegation each from both the parties took part in the two-hour long meeting at the UNDP project office here in the presence of UN Assistant Secretary General Oscar Fernandez-Taranco, who is on a special mission in Bangladesh to end the ongoing political uncertainty.
The Awami League delegation was headed by party General Secretary Syed Ashraful Islam while BNP delegation was led by its acting Secretary General Mirza Fakhrul Islam Alamgir.
Leaders of the two parties did not speak to the media about what they discussed in the meeting today.
But, Fernandez-Taranco, who wrapped up his extended six-day visit today, appreciated political parties for their "constructive" engagement.
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"It remains critical to reduce tension and to continue to engage in constructive dialogue so as to create a congenial atmosphere," Fernandez-Taranco said after the UN mediated meeting between the waring political parties.
UN Secretary General's special emissary also cautioned all parties about the consequences of the failure of the dialogue.
Fernandez-Taranco's briefing came hours after Ban phoned Prime Minister Hasina to express his concern over the prevailing situation and countrywide violence.
"Ban told the prime minister that he wants a peaceful election in accordance with the constitutional provisions," premier's press secretary Abdul Kamal Azad told reporters.
In his telephonic conversation with Hasina earlier in the day, Kerry told her that the execution of Jamaat Assistant Secretary General Abdul Quader Mollah might lead to events which could derail the parliamentary election scheduled for January 5.