Assam Governor P.B. Acharya visited the Sutarkandi border areas in Karimganj district on Sunday and held discussion with BSF officials, said police sources.
The governor has asked the BSF to keep "maximum vigil" along the winding border, a police official told IANS.
Twenty foreigners and Bangladeshis were slaughtered in a Dhaka cafe on Friday evening by Islamists, six of who were killed by security forces. A seventh terrorist was caught.
Acharya also met officials of district administration, and also talked to Border Guards Bangladesh officials, Karimganj Deputy Commissioner Manoj Kumar Deka said on Monday.
In Tripura, Governor Tathagata Roy met BSF officials on Sunday.
"We have apprised the governor about the steps taken along the India-Bangladesh border," BSF's Tripura Frontier Inspector General J.B. Sangwan told IANS.
He said: "We have alerted our troops to remain extra alert."
Tripura Director General of Police K. Nagaraj said the state government had asked the BSF to maintain a maximum alert along the border.
"Central paramilitary forces, Tripura Police and Tripura State Rifles are also keeping a close watch in the prevailing situation," Nagaraj told reporters on Monday.