Syria is three years into a civil war in which tens of thousands of people have died and millions more have been displaced.
In August last year, a chemical attack near the capital Damascus killed hundreds of people.
In August, UK MPs rejected the idea of air strikes against Syrian President Bashar al-Assad’s government to deter the use of chemical weapons.
“But every time we put off action,” Blair wrote, “The action we will be forced to take will be ultimately greater.”
Blair said: “I understand all the reasons following Afghanistan and Iraq why public opinion was so hostile to involvement.
He said action in Syria “did not and need not be as in those military engagements”.
“Where the extremists are fighting, they have to be countered hard, with force,” he said.
“This does not mean Western troops as in Iraq.
“There are masses of responses we can make short of that.
“But they need to know that wherever they’re engaged in terror, we will be hitting them.”
The Sunni insurgents, from the Islamic State in Iraq and the Levant, regard Iraq’s Shia majority as “infidels”.
After taking Mosul late on Monday, and then Saddam Hussein’s hometown of Tikrit, the Sunni militants have pressed south into the ethnically divided Diyala province.
On Friday, they battled against Shia fighters near Muqdadiya – just 50 miles (80km) from Baghdad’s city limits.
Reinforcements from both the Iraqi army and Shia militias have arrived in the city of Samarra, where fighters loyal to ISIS are trying to enter from the north.
Blair said US President Barack Obama was “right to put all options on the table in respect of Iraq, including military strikes on the extremists”.
He said the “choices are all pretty ugly, it’s true”.
“But for three years we have watched Syria descend into the abyss and, as it is going down, it is slowly but surely wrapping its cords around us pulling us down with it.”