Police in London say they are investigating complaints against a UK-based Pakistani politician to see if he has violated UK law.
Altaf Hussain, leader of the MQM party that controls Karachi, addressed supporters from London last Sunday after Pakistan's general elections.
In response to accusations of electoral fraud, he is alleged to have threatened his accusers with violence.
Mr Hussain says that his remarks were taken out of context.
London's Metropolitan Police confirmed to the BBC that an investigation had been launched "following complaints concerning comments made in a broadcast" by Mr Hussain.
Since the mid-1980s, the MQM has won every poll it has contested in Karachi and it did so again in last Saturday's general election.
But this time, it is facing strong and widespread allegations of rigging and electoral fraud.
Half a dozen smaller parties, led by former international cricketer Imran Khan's Movement for Justice Party (PTI), have been holding rallies and sit-ins to demand a re-run in Karachi.
On Sunday, addressing party workers from London, Mr Hussain responded to the allegations by appearing to threaten protesters with violence, and suggesting that if his party's mandate was tampered with, Karachi would have no choice but to separate from Pakistan.
During his speech he referred to protests taking place near the Three Swords roundabout in Karachi.
"Those people who are protesting - and grandstanding - near Three Swords - I don't want to fight or quarrel, but if I order my supporters now, they will go to Three Swords and turn them into a reality."
He added: "MQM is blamed for everything. I say, oppose us with respect and decency, and with proof, otherwise I will soon unleash my supporters."
Karachi is wracked with violence - much of it politically motivated.
Mr Hussain has since said that his remarks, which were broadcast on live TV, were taken out of context.
On Wednesday, the British High Commissioner in Pakistan, Adam Thomson, told a news conference that the UK took allegations of inciting hatred very seriously.
He said it was up to the police in London to determine whether Mr Hussain's remarks violated British laws, and whether or not he could face prosecution.
The BBC's Shahzeb Jillani in Karachi says that Mr Hussain effectively controls the city of 18 million people from his MQM headquarters in north London.
He has lived in the UK since 1991, saying his life would be at risk if he returned to Pakistan.
The MQM (Muttahida Qaumi Movement) is supported mainly by Muslim Urdu-speaking people whose families moved to Sindh province at the time of the partition of India in 1947.