Security arrangments at Gordon House in Kingston are to be reviewed following the attack in the vicinity of Britain's House of Commons last week.
Leader of Government Business Senator Kamina Johnson Smith disclosed on Friday that the issue was discussed at a meeting of the National Security Council on Thursday and will be treated as a priority.
Her disclosure came after her Opposition counterpart, Mark Golding, raised concerns about the reduced security arrangements for the sitting of the Senate when compared with the meeting of the House of Representatives.
He said that while there should be no attempt to restrict public access to Gordon House, the vulnerabilities to acts of violence must be considered.
Meanwhile, the Jamaican Senate is to write to British High Commissioner David Fitten and Speaker of the House of Commons John Bercow to express solidarity with the British people.
Fifty-two-year-old Briton Khalid Masood has been identified as the attacker responsible for mowing down pedestrians and stabbing a policeman to death outside the Palace of Westminster, where the Parliament meets.
Five people, including Masood, were killed.
The terror group, Islamic State, has claimed responsibility for Wednesday's incident.