More than a third of civilians living in areas targeted by a Syrian government offensive in the southwest have been displaced, according to the UN's latest figures.
"I look forward to a frank discussion to discuss how to arrive at a ceasefire as soon as possible", Mr Safadi said in Amman, adding that he would also be seeking ways to alleviate a worsening humanitarian situation.
On June 12, the Syrian regime, supported by Iranian militia groups and Russian air power, launched a major operation aimed at capturing opposition-held parts of southern Syria.
But it is simultaneously brokering talks with opposition fighters that have seen more than 30 towns agree to fall back under regime control so that bombing stops.
The Syrian army started the operation against the rebels in Daraa over 11 days ago, with the aim of entirely capturing the rebel-held areas due to the strategic location of Daraa near Jordan.
Nearly two weeks of fighting has forced at least 270,000 Syrians from their homes, the United Nations refugee agency's Jordan spokesman Mohammed Hawari told Reuters.
Bolstered by a string of victories across southern Syria, al-Assad's chief backer Russian Federation has been reluctant to yield to the opposition's demands.
Jordanian Foreign Minister Ayman Safadi addresses the press in Amman, Jordan, on July 2, 2018.
"The abject refusal by Jordanian authorities to allow asylum seekers to seek protection not only goes against their global legal obligations, but against basic human decency", said HRW's Lama Fakih.
The entire southwest is part of a "de-escalation zone" agreed upon past year by Russian Federation, the United States and Jordan.
The violence has pushed waves of terrified civilians out of their homes at a shocking rate, the UN's refugee agency (UNHCR) said Monday.
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Around 164,000 of the displaced people are now close to the Golan heights - an area of Syria now occupied by Israel - while 60,000 are close to the Jordanian border.
Syrians fleeing the fighting and heading towards Jordan have been denied entry, with authorities there saying they do not have the resources to deal with more refugees.
Jordan and Israel have said their borders would remain closed, even as tens of thousands of Syrians flee the government offensive.
According to the UN's humanitarian coordination office, 70,000 of those displaced have sought shelter along the border with Jordan.
"The United States, which had been a strong supporter of the Syrian opposition, particularly on the southern front in Daraa - the Trump administration has come to kind of a modus vivendi with Russian Federation, [allowing] Syrian troops to retake the area, as long as Iranian troops are not involved, or involved too much", Lesch says.
"We did not attend negotiations today".
It accused some actors of trying to secure personal interests through the agreements.
Rebels would hand over heavy weapons but would keep the rest until a "real political process" had begun.
Rebels and residents say a string of rebel towns have reached their own surrender arrangements that have allowed Russian military police to enter and patrol their towns.
Men who defected from Syria's armed forces or who did not complete their compulsory service could regularise their status with the regime within six months.