The meetings took place at Patel's residence here where several leaders had come to condole the death of his daughter-in-law Zainab Neduo.
Kamat also had a meeting with Patel, who is political secretary to Congress President Sonia Gandhi, last night.
However, both Anthony and Kamat declined to comment on their meeting.
Asked whether he was taking back his resignation, Kamat said "no comments". When further probed on whether he would meet the Congress President, he said that would happen "in due course".
Kamat had said that he has the "highest respect and regard" for Congress President Sonia Gandhi and Vice President Rahul Gandhi and "my resignation is purely on personal grounds".
Kamat, who had been Mumbai PCC chief for a long time, was reportedly unhappy over the appointment of his known detractor Sanjay Nirupam as the head of the city unit of the party.
The move had come ahead of next year's Mumbai civic elections, where Congress is hoping to dislodge the incumbent Shiv Sena-BJP combine.
Meanwhile, former Union Minister Sushilkumar Shinde expresed confidence that the leadership would resolve the issue by addressing the grievances of Kamat.
(Reopens DES 38)
Meanwhile, in a statement issued in Mumbai, Kamat denied the media reports that he had objected to the party nominating P Chidambaram to the Rajya Sabha from Maharashtra, and also the nomination of Narayan Rane for the state Legislative Council election.
Kamat also said he had no differences with Rane, and there was no question of having objected to the nomination of either leader.
He blamed the media reports on "unscrupulous rumour mongers".
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