Miliband delivered a speech on the same topic in the Indian city of Mumbai on Thursday.
He called for the closure of the US prison camp at Guantanamo Bay and the launch of new era of "democratic opportunity rather than fear and oppression".
"Democracies must respond to terrorism by championing the rule of law, not subordinating it,'' he said.
According to his article, a "fundamental look" is needed at how to prevent extremism and "terrorist violence".
"Since 9/11, the notion of a 'war on terror' has defined the terrain. The phrase had some merit: it captured the gravity of the threats, the need for solidarity, and the need to respond urgently - where necessary, with force," he wrote.
"But ultimately, the notion is misleading and mistaken. The issue is not whether we need to attack the use of terror at its roots, with all the tools available. We must. The question is how."
Britain, under Tony Blair, the former prime minister, was America's closest ally in "anti-terrorism" operations but the US-led invasion of Iraq to oust Saddam Hussein caused a backlash against Blair in Britain.
Most of the remaining British troops in Iraq are set do be withdrawn this year but Britain still has more than 8,000 troops in Afghanistan.