Salim al-Muslit, spokesman of the High Negotiations Committee (HNC), also told Reuters the opposition was sticking to its position that President Bashar al-Assad can have no role in the transition, saying "the heavy price paid by the Syrian people" would have been wasted if he remained in power. "And that happened. It happened in Europe, mainly in Germany", he claimed.
'It's against the terrorists that would infiltrate some of the immigrants to the West.
"I think the aim of Trump is to prevent those people from coming", he added, insisting the order was "not against the Syrian people".
"It's also urgent that we see where Turkey stands in light of the newfound proximity with Russian Federation and Iran", the source said, adding that it would be vital to assess how Gulf Arab Sunni states Saudi Arabia and Qatar - opposed to Assad - saw the conflict after "pulling back a little".
Trump issued a decree last month that denied entry to all refugees for 120 days, and travellers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen for 90 days.
Unlike the UAE, Syria is directly targeted by the ban on two levels: both as one of the nations singled out by the document, and as an exporter of large numbers of refugees from its ongoing civil war.
The ban was later suspended after two USA states sought to have it overturned on grounds of religious discrimination and because it had caused "irreparable injury".
Assad's presidency is an acute topic in debates on Syria's future.
The city is the so-called Islamic State's de-facto capital and has been a focus for coalition forces led by the US.
During his last interview, al-Assad seemed nearly thrilled by the restriction imposed by Trump.
"For us it is all the same, Raqqah, Palmyra, Idlib, it's all the same", Assad pointed out, stressing that it is the "duty of any government" to regain control of "every inch" of its territory.
Concerning global negotiations to end the conflict that has claimed more than 300,000 lives, Assad said Western countries had "lost their chance of achieving anything in Geneva twice".