It was the first meeting between the two leaders after they were re-elected to their respective posts for a second term.
During the meeting that lasted for more than an hour, Rao submitted memorandums on 22 issues, according to the Chief Minister's Office here.
The Chief Minister wanted the Centre to provide financial assistance to Mission Kakatiya and Mission Bhagiratha as recommended by the NITI Aayog. The planning body had recommended Rs 5,000 crore and Rs 19,205 crore for the two programmes, respectively.
KCR, as Rao is popularly known, also sought the release of Rs 450 crore as the fifth instalment of assistance for the backward districts in Telangana as per the Andhra Pradesh Reorganisation Act.
He called for the revival of the Cement Corporation of India in Adilabad district with the help of National Highways Authority of India.
KCR also urged the Prime Minister to enhance the number of judges in Telangana High Court from 24 to 42.
The establishment of an Indian Institute of Management (IIM), sanction of Indian Institute of Science Education and Research (IISER), sanction of 23 Jawahar Navodaya Vidyalayas (JNV) in new districts, early completion of pending railway projects, setting up of a steel plant at Bayyaram in Khammam district as per the Reorganisation Act and release of funds for National Investment and Manufacturing Zone (NIMZ) at Zaheerabad in Medak district were the other major demands.
The demands also included development of the Hyderabad-Nagpur and Warangal-Hyderabad industrial corridors and allotment of funds under the Prime Minister Gram Sadak Yojana (PMGSY) for upgrading 4,000 km for better connectivity in backward regions.
KCR sought the setting up of a National Institute of Design (NID) in Hyderabad. Its location was shifted to Vishakhapatnam after bifurcation.
He also sought sanction for setting up an Indian Institute of Information Technology (IIIT) under the public private partnership (PPP) model at Karimnagar.
The Chief Minister urged Modi to ensure sub-categorisation of scheduled castes in the state and enhancement of reservations for backward classes (BCs) in employment and education to 37 per cent, for SCs to 15 per cent and STs to 10 per cent.
KCR also demanded 33 per cent reservation for OBCs and women in Parliament and state legislatures and referred to the resolution passed in the state Assembly.
KCR wanted the Centre to bear the total cost instead of the ratio of 60:40 for road works in Left wing extremism affected areas.
He also sought total central funding for Tribal University as Central University in Warangal, one-time grant-in-aid of Rs 1,000 crore for the Warangal Textile Park, and declaring Ramappa Temple as a World Heritage Site.
KCR also called on Home Minister Amit Shah and Defence Minister Rajnath Singh and discussed various state-related issues with them.
( With inputs from IANS )