"I have met the Prime Minister and the Home Minister. It was a courtesy call. I informed them about the general situation in the state," Tripathi told the reporters after the meetings.
The Governor first called on the Prime Minister at his residence, and then met Shah for some 20 minutes at the North Block.
Talking to the reporters earlier on Monday, Tripathi said his visits to the Prime Minister and the Home Minister were pre-scheduled.
"I couldn't wish him personally on the swearing-in day, hence this is a courtesy visit," said the Governor whose tenure ends on July 23.
The Governor's meetings with Modi and Shah came a day after the Ministry of Home Affairs sent a strongly-worded advisory to the West Bengal government for its "complete failure" to control the unabated post-poll violence in the state. The MHA had expressed strong concerns over the tense situation in the state.
The Mamata Banerjee government says the situation in West Bengal was "under control" and "firm and appropriate action" was taken following "stray post-election clashes" in the state.
Meanwhile, BJP leader Kailash Vijayvargiya accused West Bengal Chief Minister Mamata Banerjee and her nephew of being behind the "anarchy and violence" in the state.
He said though the Centre hadn't interfered in the governance of the state, it may think about imposing President's Rule there if the violence, which began before the general elections, doesn't end.
( With inputs from IANS )