LONDON –  In a rare public speech, Britain’s top domestic spy chief Thursday called the Paris attack “a terrible reminder” that some “wish us harm” and said the evolving terror threat has become more complex because of events in Syria.

MI5 director-general Andrew Parker used a long-planned speech at the Security Service headquarters on the banks of the River Thames to say the number of Britons going to Syria to join forces with militants there is steadily rising, posing a threat as they return.

He said about 600 have gone so far, with “a significant proportion” having joined the Islamic State extremist group.

Parker, in only his second public address, refused to use the name Islamic State, but said the group threatens Britain in three ways: murdering Britons in Syria, using Syria as a base for sending members back to Britain and elsewhere to launch attacks, and using propaganda to provoke Britons inside the United Kingdom to carry out violent attacks.

The director said the group’s skill at using social media platforms means it has been able to spread its message to virtually every home in Britain, leading to a number of attacks, including many that have been thwarted by security forces and police.

The threat from Syria led Britain last summer to raise its threat level to “severe” because of the “evidence-based” conclusion that an attack was highly likely, he said.

“Outside Iraq and Syria, we believe that since October 2013 there have been more than 20 terrorist plots either directed or provoked by extremist groups in Syria,” he said, citing lethal attacks in Canada, Australia, Belgium and other countries.

He warned that al-Qaida operatives are still trying to mount large-scale attacks that must be monitored and broken up even as MI5 tries to deal with the smaller scale and “lone wolf” attacks that are a recent trend. He said the number of “crude but potentially deadly” plots has increased.