Kovind addressed the BJD MLAs and MPs at the Assembly conference hall after the chief minister's brief introduction. The meeting lasted about an hour, a legislator said.
Before the meeting, Patnaik, Kovind and Union Health Minister and senior BJP leader J P Nadda raised hands in unison, he said.
"I am very happy to be here and thankful to the BJD led by Naveen Patnaik for supporting me," Kovind told reporters after lunch with the chief minister.
Kovind was earlier welcomed by leaders of both BJD and BJP at the city airport on his arrival by a special flight.
Kovind's meeting with BJD legislators and MPs was considered as a mere formality as Patnaik had already announced his party's support to the NDA nominee describing him as a "distinguished dalit leader."
Kovind, accompanied by Nadda, spent around an hour at Naveen Niwas, the chief minister's residence near the city airport, for the luncheon meeting with Patnaik.
The ruling BJD has 117 MLAs in 147-member Odisha Assembly and 28 MPs (20 in Lok Sabha and eight in Rajya Sabha).
Kovind is also scheduled to garland the statue of Buxi Jagabandhu and meet BJP MLAs and leaders at the party's legislature party leader K V Singhdeo's residence before leaving for New Delhi.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)