CANBERRA, Australia—Australian lawmakers quashed a plan to make burqa wearers sit behind protective glass screens in Parliament, after warnings the measure could stoke tensions with the country’s Muslim population—which is already rattled by tough new counterterror laws.

The plan, proposed earlier this month by presiding lawmakers, called for Muslim women wearing head-to-toe burqas and face-covering niqabs to be forced to sit in an area usually reserved for schoolchildren as a security measure. Prime Minister Tony Abbott had...