Chennai-headquartered SpiceJet is the only domestic private airline which operates air services to Afghanistan.
"In view of the security situation in Kabul and its airport, SpiceJet has decided to temporarily suspend its Kabul flights until the situation improves," the airline said in a statement.
Gunmen had carried out a pre-dawn rocket attack on Kabul International Airport yesterday, temporarily shutting down the facility and setting off a gunbattle with security forces in which four attackers were killed.
On July 3, about 100 people on board a SpiceJet flight from Kabul to Delhi escaped a rocket attack by militants at the airport in the Afghan capital. The attack, aimed at the military airbase at the Kabul airport, was launched when the SpiceJet aircraft was getting ready for takeoff.
"In view of these incidents, we have decided to take this step as the safety of our passengers and crew is of paramount importance to us," the statement said.
SpiceJet also said that it will refund the passengers who had booked advance tickets for these flights and added that, "We will also try to request other airlines that operate to Kabul to accommodate them if they still desire to travel."