Terror suspects who attempt to leave the UK or fail to surrender their passports after being freed on bail by police could be jailed in future.
An amendment to the Policing and Crime Bill will make it an offence for someone to breach bail conditions imposed to prevent them from fleeing.
Suspects can currently be arrested but do not face any further sanctions.
It follows incidents where people have joined the so-called Islamic State group in Syria after being arrested.
They include Siddhartha Dhar, also known as Abu Rumaysah, from east London, who fronted an IS propaganda video in January. He disappeared in September 2014, shortly after being released on bail while under investigation for allegedly encouraging terrorism.
In January, Assistant Commissioner Mark Rowley, Britain's most senior counter-terrorism officer, described the existing arrangements as "weak".
The new measure would apply to suspects arrested for an offence listed in section 41 of the Counter-Terrorism Act 2008 including membership of a proscribed organisation, fundraising or encouraging terrorism.
A person would commit an offence if they breached a bail requirement not to leave the UK, surrender travel documents, or not be in possession of any travel documents, even those belonging to someone else.
A conviction will carry a maximum penalty of 12 months imprisonment and/or a fine.
It will apply in England, Wales and Northern Ireland but not in Scotland where pre-charge bail follows a different form.
Home Secretary Theresa May said: "We are determined to give the police the tools they need to fight terrorism and keep people safe.
"This tough new criminal offence will help stop suspected terrorists from fleeing the UK."
Shadow home secretary Andy Burnham said Labour had put pressure on the government to bring in changes.
"We will need to see whether Theresa May's proposals go far enough," he added. "It is essential that the police are able to request surrender of passports and travel documents as a condition of release from custody."
National Police Chiefs' Council chair Sara Thornton said the amendment should not only apply to terror suspects.
"There are real dangers of offenders breaching pre-charge bail conditions in other complex cases such as child abuse or domestic abuse," she said.