A Hamas official immediately rejected the comments as "blatant interference" in Palestinian affairs, but did not say directly whether the group planned to comply with any of the demands.
They may not be able to leave Gaza without Israeli or Egyptian permission, but their photos can.
Rival Palestinian factions Hamas and Fatah have reached agreement on aspects of their bid to end a decade-long split during talks mediated by Egypt in Cairo, officials said on Thursday.
The Palestinian cabinet met in Gaza on Tuesday for the first time since 2014 in a further step towards the internationally recognised Palestinian Authority (PA) retaking control of the territory.
The attack, which came as US envoy Jason Greenblatt was in Jerusalem for talks on relaunching the moribund Middle East peace process, drew condemnation from Israeli officials.
Palestinian prime minister Rami Hamdallah will travel to Gaza on October 2 as part of a fresh push to end a decade-long split between Fatah and Hamas, which runs the enclave, his government said Monday.
The justice ministry said the attorney general was considering prosecuting Sara Netanyahu for offences that include fraudulently procuring items, fraud and breach of trust.
The Syrian army statement said the airstrike killed two people and caused material damage near the town of Masyaf and warned against the "dangerous repercussions of this aggressive action to the security and stability of the region".
The Shamasneh family has for years been fighting a court battle against Jewish claimants who said that the building was their family property.
Israel on Wednesday backtracked from a decision to revoke the accreditation of an Al Jazeera journalist, saying he explained that comments he made last year did not amount to support for Palestinian violence.