Since 1991, the MQM political movement's leader has lived in London. Altaf Hussain sought political asylum in the United Kingdom "because of an attack on his life," according to a statement on the party's website.
London's Metropolitan Police Service said Sunday that it was investigating complaints about alleged comments made by someone associated with the MQM but did not provide additional details.
"We are in the early stages of the investigation and are assessing the information which has now been brought to our attention," the agency said in a statement. "We take all allegations of crime seriously and will respond appropriately to the concerns raised and will take action where appropriate."
The British Foreign Office condemned the Pakistani political leader's murder.
"We are deeply saddened by the recent violence in the city, including violence murderously directed against democratic political figures," a Foreign Office spokesman said.