Prime Minister's press advisor Surya Thapa also said in a Facebook post that the meeting was postponed as the two leaders need some more time for consultations.
The date of the next meeting will be decided after the two leaders hold consultations, he said.
However, a senior party leader said Oli postponed the meeting without consulting Prachanda. The Prachanda-led group had already reached the Prime Minister's official residence at Baluwatar at around 11 am and was waiting for Oli's signal to start the meeting.
Standing Committee members close to Oli did not attend the unilateral meeting convened by Prachanda later in the afternoon, party leaders said.
The meeting, which started at around 3:00 pm, lasted for one hour, they said.
Around 25 Standing Committee members were present in the meeting, the Kathmandu Post reported.
On Wednesday last week, a Standing Committee meeting was briefly held at the Prime Minister's official residence. However, the prime minister did not attend the meeting.
Subsequently, the party decided to convene another meeting a week later, on July 28, to review its activities, the government's performance, finalising division of work among party's cadres and leaders, and proposed general convention among other issues.
Meanwhile, amid the deepening rift in the party, NCP Vice Chairman Bam Dev Gautam floated a 'middle path' solution to resolve the conflict between Prime Minister Oli and Chairman Prachanda.
Gautam proposed that Oli be allowed to stay as prime minister for the remaining term of the House of Representatives (HoR), that is, two-and-a-half years, and chairman of the party until the unity general convention that Oli has proposed to hold by mid-December.
Similarly, Prachanda should be given the responsibility as the party's Chairman with all executive powers until the unity general convention of the NCP is held.
Gautam also proposed that Oli be allowed to run the government independently even though the Chairman will have all executive powers. He, however, proposed holding consultation in the party before taking any decisions on issues of national and international
The proposal also include making fixed criteria for the promotion and transfer of security officials and bureaucrats; reshuffling the Cabinet on the basis of the suggestions and consultation of the party's central secretariat; holding consultation within the party's Secretariat prior to unveiling of the government's policies and programmes and hosting party's official meeting at its central office.
Gautam also proposed holding all party meetings in its central office rather than at the official residence of the prime minister.
A bitter internal feud has been brewing in the ruling NCP since the last few weeks after top party leaders, including Prachanda, demanded Oli's resignation, saying his recent anti-India remarks were "neither politically correct nor diplomatically appropriate." They are also against Oli's autocratic style of functioning.
The differences grew further after Oli said that some of the ruling party leaders are aligning with the southern neighbour to remove him from power after his government issued a new political map incorporating three Indian territories of Kalapani, Lipulekh and Limpiyadhura.
Prachanda on Monday last week said efforts were going on to resolve the intra-party differences and ruled out an early general convention of the party as proposed by embattled Prime Minister Oli.
Oli and Prachanda have held at least eight meetings in recent weeks to sort out the differences between them. But, as the Prime Minister did not accept the condition of a one-man-one-post, the talks failed. Oli has refused to give up his post as prime minister as well as a co-chairman of the NCP.