The BCCI had expressed concern about security during the World Cup in a letter to the ICC after last month's attack in the disputed region that killed 40 Indian paramilitary troops.
"As you would expect for a global sporting event, the ICC, in partnership with the ECB (England and Wales Cricket Board) has a robust security plan in place for the men's Cricket World Cup," ICC Chief Executive David Richardson said following board meetings in Dubai.
"We work closely with the authorities in our host countries to ensure that the safety of players, officials and fans is a priority.
"Should those authorities raise the threat level of the event based on intelligence, we will of course uplift our security commitment as appropriate.
"We will continue to work with the ECB and our members throughout the build up to and during the tournament to keep everyone abreast of the situation."
The attack, the worst in the troubled area, was claimed by Pakistan-based militants and further soured relations between the bitter nuclear-armed rivals, prompting calls within India for the country to sever all sporting ties with Pakistan.
The BCCI had urged the cricket community to ostracise Pakistan in their letter to the ICC. India are scheduled to play their World Cup match against Pakistan in Manchester on June 16.
The governing body was also apprised of concerns from the World Anti-Doping Agency (WADA) regarding the BCCI's reluctance to come under the ambit of India's national anti-doping body.
"The Board unanimously acknowledged its desire to remain WADA compliant and committed to working in partnership with the BCCI, WADA and the India NADA to resolve the outstanding issues as a matter of urgency," the ICC statement said.
Former India leg-spinner Anil Kumble was reappointed as the head of the ICC Cricket Committee while restrictions imposed on Sri Lanka for alleged government interference in its administration were lifted.
(This story has been refilled to fix lit in paragraph nine)
(Reporting by Sudipto Ganguly; editing by Greg Stutchbury)
