Walid Muallem "renewed the invitation of the government to Syrian refugees living in neighbouring countries to return to their country", the SANA news agency said.
The minister "stressed the country was ready to receive them and grant them a dignified life", the agency reported, as Muallem met UN refugee agency chief Filippo Grandi.
On Friday, US President Donald Trump issued an executive order to suspend Syrian refugee arrivals indefinitely and impose tough controls on travellers from seven countries, including Syria, for 90 days.
The army's recapture of Wadi Barada from rebels comes a month after Assad's forces pushed the armed opposition out of east Aleppo, taking back control of the whole of the northern city.
Syria's rebels still hold to the northwestern province of Idlib, the Western Ghouta area outside the capital and areas in the south of the country.
Syria's conflict has killed more than 310,000 people since it erupted in 2011 with the brutal repression of anti-government protests.
The war has forced 4.8 million people to flee Syria, according to the United Nations High Commissioner for Refugees.
It is followed by Lebanon with more than one million Syrian refugees, according to the UN.
The UNHCR says Jordan has taken in 655,000 Syrians, but Amman says the number is much higher at 1.4 million.
At least another 228,000 Syrians have taken refuge in Iraq and 115,000 in Egypt, the refugee agency says.
Syrian refugees have in increasing numbers travelled to, or tried to reach, Europe, making the perilous journey overground or by sea.
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