Party leaders confirmed that Gandhi met the President but termed it as "courtesy meeting".
The Congress is keen on the post of Leader of Opposition in the Lok Sabha, saying that it is the second largest party in the lower house and was the lead party of United Progressive Alliance.
Gandhi herself has articulated the demand on Monday, saying that the Congress was single largest opposition party and had a pre-poll alliance.
The meeting came after Gandhi met party leaders on Tuesday.
UPA parliamentarians have also written to Lok Sabha Speaker Sumitra Mahajan seeking an immediate decision on the issue. The Congress has 44 members in the Lok Sabha. However, its strength is less than 10 percent of the total strength of the house, which stands at 545.
Sonia earlier met Congress party leaders on Tuesday
The Bharatiya Janata Party (BJP) leaders have cited precedents to indicate that it was not favourably inclined towards the Congress demand.
Speaking to women journalists, Law Minister Ravi Shankar Prasad said Tuesday the decision on the issue should be based on set rules and norms.
He, however, said this was his view, and a final decision will be taken by the Lok Saha speaker.
"The rule that a party needs 10 percent member strength to be the main opposition party stands since the time of (first Lok Sabha speaker) G.V. Mavalankar. The same rule has been there all these years. If it has to be changed, there has to be a reason for it."
"If the rule can be changed for 44 members, it can be changed for 30 members, or 20 members as well," he said.
Asked about the Congress statement that the party may go to the court if not given the Leader of Opposition post, the minister said: "Anyone can go to court in India."
He was referring to the Congress party assertion that it would exercise all options to ensure a "democratically correct, logical conclusion" on the issue and has not ruled out the option of approaching the court on the matter.
Prasad took a jibe at the Congress and said: "The energy and hard work they are focusing on getting the Leader of Opposition post, if they would have focused it on how they got reduced to 44, it would have helped them more."