David Cameron will return to the Middle East on Wednesday to press for an immediate humanitarian pause in the fighting.
Downing Street said Cameron was expected to raise “the importance of a two-state solution”.
The foreign secretary, who said the situation in Gaza is desperate, is due to visit Qatar, Israel, the West Bank and Turkey.
Lord Cameron, on his second visit to the region since returning to government, will continue to insist no permanent ceasefire can be agreed unless Hamas releases all the remaining hostages, is incapable of firing rockets at Israel, and an agreement exists that allows the Palestinian Authority to return to Gaza and provide services.
His visit comes as Qatar continues to try to mediate between Israel and Hamas on a plan for a two-month ceasefire that would see the release of all hostages and a large number of Palestinian political prisoners.
Some mediators believe that if such a long humanitarian pause was agreed neither side would want to return to war.
Hamas has insisted a permanent ceasefire must include the release of almost all political prisoners and the removal of the Israel Defence Forces from Gaza.
Speaking as he prepared to travel to Qatar, Cameron said a sustained ceasefire “would require Hamas to agree to the release of all hostages, Hamas to no longer be in charge of Gaza launching rocket attacks at Israel, and an agreement in place for the Palestinian Authority to return to Gaza in order to provide governance and services and, increasingly, security.”
Israel’s prime minister, Benjamin Netanyahu, has said he is opposed to the Palestinian Authority taking charge of Gaza.
Cameron will again put pressure on Israel to do more to allow aid into Gaza, but so far his requests have borne little fruit.
The Foreign Office said that in his meetings with Netanyahu and the Israeli foreign minister, Israel Katz, Cameron will call for more to be done, more quickly to increase the flow of life-saving aid into Gaza. He is also expected to raise UK concerns over the high number of civilian casualties.
Most aid agencies say only an end to the fighting will allow extra aid into the country, and technical fixes will not mean a major change.
The foreign secretary will reiterate that more crossing points need to be open for longer for aid deliveries, including the port at Ashdod and the Kerem Shalom crossing, and that water, fuel and electricity must be restored.
Cameron has met families of British hostages in London who told him they regard an end to the fighting as the top priority and believe their relatives are unlikely to survive much longer in the tunnels.
