The commission will seek the opinions of party lawmakers from both the House of Representatives, the lower chamber of the Diet, the country's parliament, and the House of Councillors, the upper chamber, as well as representatives from all 47 prefectural branches.
Under the party's rules, a presidential election will be held if requested by a majority of the total number of the party's Diet members and one representative from each prefectural branch.
Currently, the LDP has 195 Lower House lawmakers and 100 Upper House lawmakers. The total number is 342, making the majority 172.
Japanese Prime Minister Shigeru Ishiba's term as LDP president runs until September 2027.
After Friday's two-hour meeting held following the ruling bloc's dismal showing in last month's House of Councillors election, Ichiro Aisawa, head of the commission, said, "We can't go ahead with presidential election-related procedures when we've yet to complete a review of the Upper House election."
LDP Secretary-General Hiroshi Moriyama told reporters that a presidential election will be "moved up" if a majority agrees.
He indicated that the party will draw up a report on the results of the Upper House election by the end of this month.
At the general meeting, around 30 of the 250 participants presented their opinions.
According to several sources, Haruko Arimura, who chaired the meeting, suggested that the decision on the envisaged leadership election be left to the presidential election administration commission.
Many participants, mainly members of the now-defunct party faction once led by the late former Prime Minister Shinzo Abe, urged such an election to take place soon. Others, however, questioned whether the matter should be decided immediately.
After the meeting, Ishiba reiterated to reporters his intention to stay on.
Referring to the Upper House election, Ishiba said at the meeting, "I sincerely apologise for the results."
"To continue being responsible for Japan, I would like to listen to various opinions," he told attendees.
On the trade agreement reached between Japan and the United States last month, Ishiba said, "We face various issues in implementing the deal."
"We'll do everything we can so that those in each industry sector do not have any concerns," he said.