Among the issues are Gujarat's demand for an upward revision of the royalty for crude.
Patel succeeded Modi as the Chief Minister of Gujarat after the latter moved to the Centre last month as the head of the NDA government.
Patel also paid courtesy visits to Vice President Hamid Ansari and Speaker of Lok Sabha Sumitra Mahajan, official sources said.
She was accompanied by Chief Secretary Dr Varesh Sinha and Chief Principal Secretary to Chief Minister K Kailashnathan.