Indian police issued the alert, saying that four members of the group had entered the city and were suspected to be plotting an attack over the holidays.
Himanshu Roy, Mumbai's joint commissioner of police, said the four suspected terrorists had "sneaked into the city to carry out extremely dangerous activity," according to CNN. The men are reported to be 20 to 30 years old.
The Pakistan-based Lashkar-e-Tayyiba is listed as a terrorist organization by the U.S. State Department and is believed to be behind the 2008 Mumbai shooting and bombing attacks, which killed at least 175 people.
Mohammed Ajmal Kasab of Pakistan, the lone surviving terrorist of the 2008 attacks, was sentenced to death this year by an Indian court for his role in the attacks, but his lawyers appealed his sentence.
Lashkar-e-Tayyiba is also believed to have orchestrated the city's 2006 train bombings.
The 2006 and 2008 attacks raised tensions between nuclear-armed neighbors India and Pakistan. Analysts fear another such terrorist attack could escalate tensions and deteriorate regional security.
Security has been increased at popular tourist spots and hotels. The Taj Mahal Palace and Tower Hotel, the site of some of the worst carnage in the 2008 attacks, is reported to be under heavy security.
Mumbai has been a target of terrorist attacks due to its high population density and status as India's financial capital.
