NCP is the single largest party with 28 seats while Congress has 22 seats in the 78-member upper house.
"NCP has declared outside support to the minority BJP government and has also assured help during the floor test. How can the party seek the leader of opposition's post," Thakre asked.
NCP leaders had earlier said that they would stake claim to the post.
On whether Congress will oppose the NCP's claim in the house, he said it would take a stand when the situation warrants.