"It is important to not let this moment slip," United Nations special representative Volker Perthes told reporters in Khartoum. "We are asking everybody to work with one another in good faith."
Since the coup, Sudan has been rocked by deepening unrest -- near-weekly protests, a violent crackdown that has killed over 100 people, and a tumbling economy.
The military takeover derailed a fragile transition to civilian rule that had been established following the 2019 ouster of long-serving president Omar al-Bashir.
The UN, African Union and regional bloc IGAD have since March been pushing for Sudanese-led talks to break the political stalemate.
On Tuesday, Burhan hailed the talks as a "historic opportunity" and called on political factions "to not stand as a stumbling block".
Burhan last month lifted the state of emergency imposed since the coup, and authorities have in recent weeks released multiple civilian leaders and pro-democracy activists.
Perthes welcomed the measures, but said "more can be done".
Wednesday's talks were attended by military officials, representatives from several political parties, and senior members from ex-rebel groups.
But Sudan's main civilian bloc, the Forces for Freedom and Change (FFC) -- which was ousted from power in the coup -- as well as the influential Umma party have refused to take part.
Members from the resistance committees, informal groups which emerged during the 2019 protests against Bashir and which have led calls for recent anti-coup rallies, were also absent.
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