Syrian government forces and their allies have been on the offensive since late October in Hama and provinces, capturing almost 100 villages from insurgent groups, including the -linked Levant Liberation Committee.
Government fighters have seized a string of villages in the southeast of the province since launching their offensive on December 25.
The U.N.'s Under-Secretary-General for Humanitarian Affairs Mark Lowcock, in Damascus, said he was "deeply worried" about civilians caught up in the violence in Idlib.
Syria has been embroiled in a civil war since 2011.
On Wednesday, more than two dozen people were killed in the government bombardment of eastern Ghouta and rebel shelling of the capital itself.
The government-controlled Syrian Central Military Media said on Wednesday that Syrian troops are fighting militants, including members of al-Qaida-linked Levant Liberation Committee, in different areas near Abu Zuhour.
Zeid also expressed "grave concern" about the situation of an estimated two million people in the Idlib governorate of Syria where tens of thousands of civilians have been displaced due to increased clashes between government forces and its allies, and the Hay'at Tahrir Al-Sham alliance of armed opposition groups that controls much of the Idlib area.More news: Why Liverpool have best chance of ending Manchester City's unbeaten domestic run
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Idlib is the largest remaining territory in rebel hands, and its population is swollen with more than 1.1 million refugees who have fled fighting from other areas in Syria, according to the United Nations.
Numerous newly displaced brought only the belongings they could carry, the committee said, adding that one mother of two twin babies recounted the initial panic of fleeing the airstrikes. "The fear affected our brains", said the mother, quoted by the IRC.
The Observatory on Monday said 27 civilians were killed in the attack, including 14 children. The baby was unharmed, she added.
The Observatory confirmed insurgents have retaken several villages from government troops and said 11 pro-government fighters were captured.
Syrian regime forces faced fierce resistance from jihadists as they fought to capture a key airbase in the northwestern province of Idlib on Thursday, a monitor said.
The Syrian government hit back on Thursday against French criticism of its military campaign in rebel-held Idlib, saying it was targeting terrorist groups that were not party to an agreement to reduce fighting in the rebel-held region. Lowcock, in Damascus, said he would like to see "more detailed evidence" about the claims, and said it would be topic of continued discussion with government officials.
Turkish presidential sources said that President Recep Tayyip Erdogan spoke to his Russian counterpart Vladimir Putin on the phone Thursday and told him that Moscow should stop Syrian attacks on its opposition in Idlib and eastern Ghouta near Damascus, if he wants peace negotiations to succeed.