It comes after Prime Minister Benjamin Netanyahu said Israel would maintain “overall security responsibility” in Gaza for an “indefinite period” after defeating Hamas.
Speaking at a G7 meeting in Japan, Mr Cleverly indicated that the UK wanted a “peace-loving Palestinian leadership” in the strip.
The United States is opposed to any reoccupation of the territory, from which Israel removed soldiers and settlers in 2005.
The US has suggested that a revitalised Palestinian Authority (PA) could govern Gaza.
But the internationally recognised PA, whose forces were driven out of Gaza by Hamas 16 years ago, says it would only do so as part of a solution that creates a Palestinian state in Gaza, the West Bank and east Jerusalem.
Mr Cleverly said: “What we’re seeing at the moment is an Israeli military operation in Gaza. Their explicit aim is to remove Hamas as the government of Gaza.
“The UK Government’s position has long been that we want to see a Palestinian leadership for the Palestinian people, committed to peace and committed to a two state solution.
“In the short term, it is inevitable that Israel, because they have the troops in Gaza, will need to have a security responsibility.
“But our view is as soon as practicable, a move towards a peace-loving Palestinian leadership is the most desired outcome.
“The UK position is clear. It is unchanging. We want to see a two-state solution where a Palestinian state and an Israeli state are living side by side in peace and prosperity.”
The meeting of G7 foreign ministers ended with a statement condemning Hamas, supporting Israel’s right to self-defence and calling for “humanitarian pauses” in the fighting to speed up aid for desperate Palestinian civilians in the Gaza Strip.
US secretary of state Antony Blinken, Mr Cleverly and ministers from Canada, France, Germany, Japan and Italy emphasised that they “support humanitarian pauses to facilitate urgently needed assistance, civilian movement and release of hostages”.
While there, politicians also stressed that the conflict in the Middle East would not distract from the war in Ukraine.