Todd Lyons and other senior officials were questioned by lawmakers on the House committee on homeland security after ICE agents shot and killed two American citizens as part of US President Donald Trump's immigration crackdown in Minneapolis.
The deaths of Alex Pretti and Renee Good sparked outrage across the country.
Representative Nellie Pou - who represents New Jersey's ninth district, which includes the MetLife Stadium where the World Cup final will be played - asked Lyons, external if ICE would commit to pausing operations around matches and other Fifa events.
She claimed that visitors' confidence was "plummeting and jeopardising the World Cup".
Lyons responded by insisting that ICE was "dedicated to securing that operation, and we are dedicated to the security of all of our participants as well as visitors."
Pou said: "You realise that if [fans] feel they are going to be wrongfully incarcerated, wrongfully pulled out, that is going to hurt this entire process?"
"Yes ma'am, and ICE is dedicated to ensuring that everyone that visits the facilities will have a safe and secure event," replied Lyons.
Both US citizens, Good and Pretti were each shot multiple times during enforcement operations.
Their deaths - and ICE's broader action - caused outrage in Minneapolis where some 3,000 agents were deployed at Trump's direction to crack down on illegal immigration.
Some of those agents have since left the city.
Last month fan group Football Supporters Europe (FSE) told BBC Sport it was "extremely concerned by the ongoing militarisation of police forces in the US" before this summer's World Cup in North America.
The European Democratic Party (EDP) also said it may ask national football federations to consider pulling out of the tournament if safety guarantees are not forthcoming.
Fifa has said the safety and security of fans and participants is its "top priority", adding it works closely with local authorities "to plan, co-ordinate and deliver comprehensive security measures for the tournament".
The US is due to host 78 matches across 11 cities, with co-hosts Canada and Mexico hosting 13 matches each.
