Pawar, NCP chief and Union Agriculture Minister and Heavy Industries Minister Patel, kept themselves away from the Cabinet meeting in the evening and were closeted with some senior party leaders at Pawar's residence at the same time.
Pawar is said to be miffed over the denial of Number 2 status in the Cabinet after the exit of Pranab Mukherjee.
After the meeting, NCP spokesman D P Tripathi strongly denied reports of resignation.
Asked by reporters as to why the ministers kept away from the Cabinet meeting, he said "the pecking order was not the case as Pawar had never sought any position. Issues (for skipping the meeting) were much higher."
Sources in the party said the resignation offers have been made to make the Congress go into the issue and talk to allies on their concerns. The Congress cannot take the allies for granted, the sources said.
The NCP leaders are expected to meet again tomorrow on the issue.
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The Agriculture Minister who sat in the No. 2 seat in the first Cabinet meeting after Mukherjee's resignation but in the next meeting the seat was taken by Defence Minister and senior Congress leader A K Antony.
This was interpreted as Congress' way of sending a message that Antony was the virtual No. 2 in the government. To add to NCP's anger, Pawar's name had appeared in the No. 2 position in the list of Cabinet ministers on the Prime Minister's website but the list itself was removed from the official websites of the PMO and Cabinet Secretariat.
The NCP action came on a day the UPA presented a united picture during the voting for Presidential election.
NCP had on Saturday last also stayed away from the UPA meeting on Vice Presidential poll candidate.