New Delhi, India (CNN) -- Police issued an alert Thursday in Mumbai, saying four members of a militant group had entered the Indian city and were suspected of plotting violence on the Christmas and New Year's holidays.
Himanshu Roy, Mumbai's joint commissioner of police, said the suspected terrorists belong to Lashkar-e-Tayyiba, the Pakistan-based group that was blamed for a violent siege on Mumbai in November 2008.
The four men were identified as Abdul Kareem Moosa, Noor Abu Ilahi, Walid Jinnah and Mahfooz Alam, each between 20 and 30 years old. At a news conference, Roy released a sketch of Jinnah.
Roy said the four recently "sneaked into the city to carry out extremely dangerous activity."
He had no information on their nationalities.
A source familiar with the police investigation told CNN that India's Ministry of Home Affairs issued a bulletin earlier this week to police departments around India warning of possible terror attacks in Mumbai and Ahmadabad, further north in the western state of Gujarat.
Specific to Mumbai, the bulletin called for beefed up security at luxury hotels, tourist hubs, churches and consulates, especially those of the United States and European nations, the source said.
The bulletin warned of possible carjackings and vehicle-borne explosives.
Mumbai police were restricting traffic starting Thursday in and around the Taj Mahal Palace and Tower hotel, one of the landmarks that had come under attack in 2008, several Indian newspapers reported.
"All roads, except for two access points, leading to the Taj hotel will remain closed from Thursday," Nawal Bajaj, a police official, told The Times of India. "This is being done due to a specific intelligence alert. This arrangement will continue for the next 15 days."
Bajaj said every food truck entering the hotel grounds will be checked and police will conduct background checks on hotel suppliers.
Additional security has been arranged for crowded destinations like the seaside Gateway of India, a popular spot for New Year's celebrations.
Lashkar-e-Tayyiba is on the U.S. State Department's list of terrorist organizations, and last month the U.S. Treasury said it is prohibiting Americans from "engaging in any transactions" with that group.
The Treasury specifically cited Azam Cheema, who helped train operatives for the 2008 Mumbai attacks and was the "mastermind" behind Mumbai train bombings carried out by Lashkar-e-Tayyiba in 2006.
Mumbai has been the target of several terrorist attacks in the past few years, including train bombings in 1993 that killed 257 people. The most shocking and freshest in the minds of Mumbaikars is the 2008 siege.
In the coordinated onslaught, 10 gunmen stormed three hotels, a train station and a Jewish cultural center, killing 164 people.
Only one of the gunmen, Mohammed Ajmal Kasab of Pakistan, survived the attack. He has been convicted of murder, conspiracy and waging war against India. His lawyers have appealed his death sentence to a higher court of Mumbai.
Last month, Indians marked the second anniversary of the attack with prayers, a march for peace and a wreath-laying ceremony.
Indian Prime Minister Manmohan Singh vowed renewed efforts to track down those behind the assault.
"We will never succumb to the designs of our enemies," he said. "We pledge to redouble our efforts to bring the perpetrators of this crime against humanity to justice."
The attack on India's largest city and its financial hub derailed the fragile peace process between nuclear-capable arch-foes India and Pakistan. Under U.S. pressure, the two neighbors resumed talks this year in a bid to restart a full dialogue, but progress has been slow.
CNN's Harmeet Shah Singh and Ram Ramgopal contributed to this report.