"By not doing so, we are in grave danger of sending a message to the youth today that the mass murder of civilians can be justified if the right grievances are cited," the group said in a letter to Brown, Muslim News reported.
"In the current political climate there is a real danger that young people who witness the impotence of institutions that are supposed to be protecting innocent life, will turn to other organizations in an effort to make their voices heard and the violence stop," the letter further warned.
The YMAG was launched in October 2008 to voice the views and opinions of young Muslims in four key areas identified by the government - on discrimination, increasing employment levels, Preventing Violent Extremism and boosting civic participation.
"As a group, we have defined 'violent extremism' as being the indiscriminate killing of innocent people, wherever and by whoever this is perpetrated," said the group, composed of 22 young Muslim leaders from different parts of the country.
"With over 450 innocent Palestinians killed in Gaza at the hands of the Israeli Government, the British Government must see this as an act of 'state terrorism' and as a form 'violent extremism', it must be clearly condemned," the letter told the prime minister.
"Our failure to take clear action also jeopardizes our efforts to achieve the objectives of the PREVENT agenda, as we will be seen to be inconsistent and hypocritical in our approach," it warned.
YMAG said it looked forward to working with the government to help prevent all acts of violent extremism and create a cohesive and harmonious society both in Britain and across the wider world.
It expressed hope that the British prime minister would "take decisive action to assist us in achieving this goal."