The spokesman said Annan hopes the move "will lead to further progress towards improving conditions for the divided population and the resolution of all outstanding issues between India and Pakistan."
Meanwhile, the US State Department has also congratulated the leaders of Pakistan and India "for their vision in launching this initiative on behalf of the people of Kashmir."
In a comment, a senior State Department spokesman said that "attempts to frustrate this bus service are an affront to those Kashmiris who want to unite families long divided by the LoC, and must not be allowed to succeed."
FOLLOWING IS THE TEXT OF THE COMMENT: "The United States is very pleased by the completion of the first bus journey across the Line of Control in more than 50 years. We applaud the courage of the Kashmiri passengers who made this historic journey of reunification in the face of threats from those who do not want to see peace in Kashmir.
We congratulate the leaders of Pakistan and India for their vision in launching this initiative on behalf of the people of Kashmir.
The hundreds of Kashmiris who cheered the opening of the bus service demonstrated the strong support on both sides of the LoC for the 'Peace Bus.'
The grenade attack along the route of the bus service by militants was an attempt to disrupt the service and intimidate the Kashmiri passengers of this bus line.
Attempts to frustrate this bus service are an affront to those Kashmiris who want to unite families long divided by the LoC, and must not be allowed to succeed."