Gandhi met Advani after he and Congress MPs disrupted the lower house demanding a debate on communal violence, sources said.
The Bharatiya Janata Party (BJP) leader, according to sources, was upset due to the disruptions in the house, and wanted the floor managers of the National Democratic Alliance to resolve the issue.
The Congress vice president Wednesday led party members to the speaker's podium to protest the government's refusal to agree to an immediate discussion on the increasing incidence of communal clashes in the country.
The Lok Sabha witnessed continuous protests from opposition parties, including the Congress, Samajwadi Party and Rashtriya Janata Dal over their demand for discussion on the issue.
Finance Minister Arun Jaitley said they were making an issue out of a non-issue.
"Why has Congress made an issue of this non-issue? Reason is clear, a section of the party, unable to lead, is facing a palace coup," he said.
Rajiv Pratap Rudy of the BJP said: "Rahul Gandhi calling the speaker 'partial' is unfortunate and avoidable. It is pure frustration and nothing else."
Parliamentary Affairs Minister M. Venkaiah Naidu said the government was ready for any debate.
"There is peace in the country, let peace prevail in parliament. We are ready for any debate," Naidu said.