The move came a day after four men were arrested in the Copenhagen area on suspicion of having joined the Islamic State jihadist group while in Syria. Two other individuals were later arrested on weapons charges and police on Friday decided to press charges against one more man, bringing the total involved in the case to seven.
"It will simply be prohibited to set foot in certain areas," Justice Minister Søren Pind said in a statement.
"That way we make it easier to punish people who travel to, for example, Syria to join or support a terror organisation," he added.
Under the proposal, Danish citizens and residents would face up to six years in jail if they travel to an area where a "terror organisation" is taking part in an armed conflict.
The maximum penalty for "letting oneself be recruited to commit acts of terrorism" would also be raised to 10 years from six, and to 16 years for those who have taken part in combat operations.
Some groups of people, such as journalists and those working for public authorities, could be exempt from the ban.
The opposition Social Democrats and the anti-immigration Danish People's Party said they would back the minority government's proposal, which would give it majority backing in parliament.
The proposal is to be put before parliament in the coming months and, if approved, will go into force on July 1.
But it has been criticised by experts who said it was unlikely to deter radicalised youth from travelling to Syria.
"Those who want to fight for the Islamic State group will be indifferent to any prison sentence," Tore Hamming, an expert on militant Islamism at the European University Institute in Florence, told Danish news agency Ritzau.
"They already lack confidence in the Western state model or our laws," he added.
Since March last year, Danish authorities have been able to seize passports and issue travel bans belonging to those suspected of planning to participate in armed conflict abroad.