The envoys met deputy leader of Brotherhood, Khairat El-Shater, just after midnight, having received permission from the prosecutor general to visit him at Tora prison, south of Cairo, the Egyptian state news agency reported. (Agencies)
The report citing "an informed source" contradicted an earlier government denial of a visit by the envoys from United States, European Union, United Arab Emirates and Qatar.
The news agency gave no further details. Earlier, a Doha-based news channel reported that the meeting had taken place. The reports could not be independently confirmed.
Shater is deputy leader of the group that propelled Mursi to office last year in Egypt's first democratic presidential election. Seen as the Brotherhood's main political strategist, he was arrested after Mursi's downfall on charges of inciting violence.
The international mediation effort is helping to contain the conflict between Mursi's Islamist backers and the interim government installed by the military that overthrew him on July 3, following mass protests against his rule.
The army-backed government said on Sunday that it would give mediation a chance but warned that time was limited.
Thousands of Mursi supporters remain camped out in two Cairo sit-ins, which the government has declared a threat to national security and pledged to disperse.
The authorities say the Brotherhood has incited violence, accusing it of engaging in terrorism - a charge the movement denies as it grapples with one of the toughest moments in its 85-year history.
The crisis has left Egypt, the Arab world's biggest nation, more dangerously divided than at any point since the downfall of US-backed strongman Hosni Mubarak in 2011 and raised questions over the future of its nascent democracy.
Mursi became Egypt's first freely elected leader in June 2012. But fears that he sought to establish himself as a new dictator coupled with a failure to ease economic hardships afflicting most of its 84 million people led to huge street demonstrations on June 30, triggering the army move.
Court sets date for trial of Shater, others
The military has laid out a plan that could see a new head of state elected in roughly nine months. The Brotherhood, an Islamist movement that spent decades in the shadows before Mubarak's downfall, says it wants nothing to do with the plan.
However, diplomats say the group knows Mursi will not return as president and wants a face-saving legal formula for him to step down that guarantees it a stake in the political future.
Almost 300 people have been killed in political violence since Mursi's overthrow, including 80 shot dead by security forces in a single incident on July 27. Much of the Brotherhood's leadership is in custody.
On Sunday, a Cairo court announced that the top leader of the Brotherhood and two other officials including Shater would go on trial in three weeks' time for crimes including incitement to murder during protests in the days before Mursi was toppled.
That could complicate efforts to launch a political process, encourage national reconciliation and avert further bloodshed.
The interim administration has said that it wants political reconciliation to include the Brotherhood but says the group must first renounce and halt violence.
Suggesting an appetite for compromise, a spokesman for the Mursi camp said on Saturday that it wanted a solution that would "respect all popular desires," an apparent recognition of the strength of the protests against his one year in power.
During a meeting with US Deputy Secretary of State William Burns and European Union envoy Bernadino Leon on Saturday, the pro-Mursi delegation also said that they would be willing to negotiate with politicians that backed Mursi's ouster.
But they are also seeking the restoration of a constitution suspended when Mursi was deposed and want the military, together with army chief General Abdel Fattah al-Sisi, out of politics.
Mursi is being held at an undisclosed location and facing a probe into accusations including murder.
The envoys met deputy leader of Brotherhood, Khairat El-Shater, just after midnight, having received permission from the prosecutor general to visit him at Tora prison, south of Cairo, the Egyptian state news agency reported.