The Governor first called on the Prime Minister, describing it as a "courtesy meeting", and then met Shah for some 20 minutes at the North Block.
Tripathi told the media that he had informed the Minister about the situation in the state where violence has continued between supporters of the BJP and the ruling Trinamool Congress since the general elections.
Tripathi declined to say anything more.
Before leaving for Delhi, Tripathi said he would brief Modi about the killings in Sandeshkahali on Saturday if it came up for discussion.
"It will be a courtesy meeting. But in the meantime the incident (at Sandeshkhali) happened on June 8.
"If the issue is discussed, I will apprise him whatever I know about it. But basically, it is a courtesy meeting," Tripathi added.
A major clash broke out between Trinamool and BJP workers in Sandeshkhali's Hatgachi area over the removal of saffron party flags.
The police have confirmed three deaths two from the BJP and one from Trinamool Congress in the incident. But the two parties claim at least eight people died.
The central government has already sent an advisory to the state government expressing "deep concern" over the continuing violence and alleging failure on the part of the law enforcement machinery of the state to maintain the rule of law.
The advisory, from the union Home Ministry, directed the state government to uphold law and order and public tranquillity.
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.
( With inputs from IANS )