The protests have intensified as Israel continues its retaliatory bombardment of Gaza.
Emma Little Pengelly said that while concern for the safety of civilians is understandable, some of the protest activity has strayed into support for further terror attacks.
“While it is right and understandable that people are seriously concerned about civilians, a concern we all share, the demonstrations have gone beyond this in many cases to support terrorist actions and calling for more,” the Lagan Valley representative said.
“This is entirely unacceptable and must be tackled.
"There is no place for the glorification of terrorism on the streets of this United Kingdom.”
Ms Little Pengelly said: “On 16th October the Prime Minister reassured my colleague Sammy Wilson that ‘police across the United Kingdom will use all tools at their disposal’ to stamp out such incidents and ‘arrest those who perpetrate these acts’.
"This hasn’t always happened however, whether on the streets of London or Londonderry.
"Despite the strong words from the Prime Minister, the current legislation is not robust enough to deal with such incidents, and there is an unwillingness to attempt to even enforce it.”
Ms Little Pengelly said: "Ministers have talked about it being a question of both legality and values. However, the nation’s values will be influenced by the laws which govern us. The government needs to both strengthen that legislation and ensure there is clear direction across all parts of the UK as to how it can be enforced.”
Meanwhile, Ms Pengelly’s DUP colleague Diane Dodds said those behind calls to have Hillary Clinton removed as Chancellor of Queen’s University Belfast are motivated by “anti-Israeli sentiments”.
The Upper Bann MLA said the protestors “may try to claim it’s about the specific comments she has made most recently, but the true motivation appears to be simply that she is a vocal and prominent supporter of the state of Israel”.