(CNN) — Indian officials said they believe “elements in Pakistan” are somehow involved in the attacks on Mumbai — a claim Islamabad disputes — but one official said it will be difficult to ascertain details before the situation is over.

“The preliminary investigation indicates that some elements in Pakistan are involved,” said Pranab Mukherjee, India’s foreign affairs minister.

“I can’t tell you the details since the investigation is going on,” he said. “Until the investigation is complete, it will be difficult to say where they came from and how they came.”

Indian Prime Minister Manmohan Singh also indicated that the gunmen came from Pakistan’s largest city, Karachi, in a telephone call with his Pakistani counterpart Friday.

Karachi police have said they have no evidence the attackers departed from their city.

Pakistani Prime Minister Yousuf Raza Gilani condemned the “heinous crime” and said he would send the chief of his country’s intelligence agency to help with the investigation.

A group calling itself the Deccan Mujahedeen has claimed responsibility for Wednesday’s coordinated and deadly attacks in southern Mumbai, but security analysts know next to nothing about the group, and some discount its claim.

Intelligence officials from India and beyond are trying to determine who the attackers were and what their motivation was. The attacks left at least 155 people dead and more than 300 injured at a nine sites across Mumbai.

“Deccan Mujahedeen seem to be this amazing group that has come out of nowhere, that has been operating under the radar for all this time, yet able to mount such a sophisticated and well-coordinated attack,” security analyst Will Geddes said.

That is unlikely, he suggested.

One highly placed intelligence official who has been briefed on the attacks said that the head of the operation is a Bangladeshi and that the militants are Indians, Kashmiris and Bangladeshis. The Indian military has sustained a large number of casualties, the source said.

A U.S. counterterrorism official said the level of sophistication in the attack leads officials to believe that it might be tied to Lashkar-e-Tayyiba (Army of the Pure), an Islamic extremist group that has carried out previous attacks in India.

The group denied involvement in the attacks Thursday.

“The LeT has no links with Deccan Mujahedeen,” said a caller identifying himself as Abdulla Ghaznavi, a spokesman for LeT, as the group is known. He said the group condemns the Mumbai attacks and demands an international inquiry into them.

LeT is thought to be responsible for a string of bombs that ripped through packed Mumbai commuter trains and platforms in July 2006, killing more than 200 people.

The U.S. State Department said LeT has several thousand members in the Pakistan-controlled part of Kashmir and calls it one of the three largest and best-trained groups fighting against India.

Kashmir, divided between India and Pakistan and claimed by both, has been wracked by an 18-year separatist campaign that authorities say has left at least 43,000 dead.

The counterterrorism official mentioned another group, Jaish-e-Mohammed, which is based in Pakistan and, like LeT, fights for the end of Indian rule in Kashmir. Either group is capable of using fighters with handheld weapons and grenades against fixed targets, the official said.

What is different is the deliberate targeting of Westerners, the official said.

A senior U.S. official said, “Our attention is focused on the sophistication of the execution of the attacks.”

The sophistication was “to the extent it does not seem like Deccan Mujahedeen could carry it off, so the question is, did they have outside help?” the source asked.

U.S. sources said the attacks do not seem to point to al Qaeda, which usually launches mass-casualty attacks using vehicles or suicide vests and does not usually take hostages.

Another group mentioned as a possible culprit is the Indian Mujahedeen, a Muslim militant group that emerged about a year ago. Despite its relatively new status, the organization is thought to have the organizational capability to carry out such attacks, said Paul Cruickshank, a fellow at the Center on Law and Security at New York University’s School of Law.

The group has declared “open war” against India in retaliation for what it said was 60 years of persecution against Muslims and the country’s support of U.S. policies.

In September, the group said it was behind a series of explosions that ripped through busy marketplaces in New Delhi, killing 24 people and wounding about 100. The group also claimed responsibility in May for near-simultaneous bomb attacks that killed 63 people in the northwest city of Jaipur.

Officially, the Indian government has said no one has claimed responsibility for this week’s Mumbai attacks. The Deccan Mujahedeen claims came in e-mails to Indian media outlets.

Deccan refers to the Deccan Plateau, which makes up the majority of the southern part of the country. “Deccan” is an Anglicized form of “dakkhin,” which means south. Read more on the international reaction

Mujahedeen translates into “those engaged in the struggle for jihad.” Although “jihad” in Islam can mean any endeavor that requires dedication, the term has taken on a militant tone in recent years.

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