Front-runner Abdullah escaped an assassination attempt on Friday when two bombs blew up outside a hotel where he had just staged a rally, killing 12 people and wounding 40.
"Initial investigation indicates that an intelligence agency of a foreign country and LeT have been involved," said a statement from Afghan President Hamid Karzai's office after he chaired a security council meeting at the presidential palace on Sunday.
"The terrorists of this group are after disrupting the Afghan presidential election."
The ministers of the security sector briefed the meeting on the attack against Abdullah.
Afghanistan usually speaks of unnamed foreign powers when it wants to hint at a suspected Pakistani role in an incident.
Kabul has often accused the powerful Pakistani intelligence agency, the Inter-Services Intelligence (ISI), of orchestrating attacks in the country, including one on Kabul's Serena Hotel in March in which militants shot dead nine people, including foreigners.
The LeT is founded by Hafiz Saeed, who has a $10 million U.S. bounty on his head. The group, which has been accused of attacking Indian targets in Afghanistan, was also blamed for the 2008 commando-style raid on Mumbai that killed 166 people.
Security is being ramped up so the two candidates in Afghanistan's presidential election run-off next week can continue campaigning after the attempt to assassinate Abdullah, an Interior Ministry spokesman said earlier on Sunday.
© Thomson Reuters 2014