UN Secretary General Ban Ki-moon on Monday deplored Syria's cross-border fire into Turkey, which killed some Syrian refugees fleeing the continued conflict in their country.
He also criticized Syria's firing into Lebanon, where some Syrians have taken refuge.
Ban said in a statement that he was "alarmed by reports of continued violence and human rights violations in Syria, which resulted in an increased flow of refugees into neighbouring countries."
"The secretary general reiterates his demand that the government of Syria immediately cease all military actions against civilians and fulfil all of its commitments made through joint special envoy Kofi Annan," Ban said.
"The timeline for the complete cessation of violence endorsed by the Security Council must be respected by all without condition."
Damascus had agreed with Annan to withdraw troops from populated areas and stop use of heavy weapons against the opposition by Tuesday. The armed opposition had also agreed to reciprocate to Damascus within 48 hours and both sides were to end hostilities by 6 am local time (0300 GMT) Wednesday.
Turkish Foreign Minister Ahmed Davutoglu had called Ban on Monday to convey his government's "utmost concern" over the recent developments, including cross-border fire into Turkey that caused deaths and injuries suffered by Syrian refugees.
Ban expressed appreciation to countries that are neighbours of Syria for their hospitality given to Syrian refugees, saying that the UN had immediately mobilized emergency assistance to help them.
"We stand ready to provide further humanitarian assistance," Ban said.