US Edition Mr Hague was speaking during a brief lull in the violence as Egyptian prime minister Hisham Kandil visited the enclave, which has seen a deadly exchange of rockets and airstrikes in recent days.
Prime Minister David Cameron last night spoke by telephone with his Israeli counterpart Benjamin Netanyahu to discuss the situation following Israel's assassination of Ahmed Jabari, the Hamas military chief, in a drone strike on his car on Wednesday.
Downing Street said that the PM made clear that Hamas bears principal responsibility for the crisis, but called on Israel to do everything it could to avoid civilian casualties.
The conflict has been intensifying over recent weeks, but flared up dramatically in the wake of the Israeli strikes against senior Hamas figures.
Hundreds of rockets have been fired into Israel, with three people killed in the town of Kiryat Malachi - about 15 miles north of Gaza. Palestinian militants also fired rockets at Israel's commercial and cultural capital Tel Aviv for the first time.
Israel has responded with airstrikes, with at least 18 Palestinians, including some civilians, reported to have died since Wednesday.
Mr Netanyahu has warned that his country is prepared to extend its operation against Hamas, sparking fears of a repeat of the ground incursion four years ago in which hundreds died.
Mr Hague told BBC Radio 4's Today programme that there had been ''a large increase'' in rocket attacks on Israel from Gaza over recent weeks.
And he added: ''What Israel has done is obviously the Israeli response to that. The thing that would bring this most quickly to an end would be for Hamas to stop launching rockets at Israel.
''But of course, there are also responsibilities on Israel. I spoke to the Israeli foreign minister yesterday afternoon to urge the Israelis to do their utmost to reduce tension, to take every opportunity to de-escalate the situation and observe international humanitarian law, to avoid civilian casualties.
''Both sides have a responsibility to try to bring this to an end.''
Mr Hague said he also spoke to the Egyptian foreign minister last night to urge him to use his country's influence to try to negotiate a ''meaningful'' ceasefire.
Calling for a ''real drive'' to revive negotiations, Mr Hague said: ''The onus now is on Palestinians to reconcile with one another, Hamas to commit to a deal instead of terrorism, Israel to seize that opportunity and the outside world - including the US - to help negotiations to restart.
''The easiest, best contribution to ending this would be for Hamas to stop launching the rockets and to take control where other people are launching rockets at Israel, but we do stress ... we want Israel also to take every opportunity to de-escalate.''
Asked about the prospect of a ground attack, Mr Hague said: ''Israel does have to bear in mind that it is when ground invasions have taken place in previous conflicts that they have lost international support and a great deal of sympathy around the world. There is a cautionary lesson from previous ground invasions.''
Asked whether Britain would condemn a ground offensive, Mr Hague said: ''We will see what the situation is. This depends on the actions of two sides, not just one side.''
Downing Street said that in last night's call, Mr Cameron told Mr Netanyahu he was ''extremely concerned by the dangerous situation and deeply sorry for the loss of civilian life on both sides''.
A Number 10 spokesman added: ''He said the rocket attacks from Gaza into southern Israel by Hamas and other armed groups were completely unacceptable and that the increasing frequency of rocket attacks in recent days was the immediate cause of the situation.
''He made clear that Hamas bears the principal responsibility for the crisis.''
Mr Cameron hopes to speak to the president of Egypt, Mohammed Morsi, today on the same issue.
Shadow foreign secretary Douglas Alexander said: ''The priority must be an immediate end to the violence to avoid a spiral downwards to even greater suffering. Escalating tension serves no one's interest.''
Former prime minister Tony Blair, who last night missed a talk with former United States president Bill Clinton in central London to be at the bedside of his father Leo who is seriously ill, urged Hamas to stop its rocket attacks on Israel.
The Middle East envoy told Sky News: ''The only way you are going to get a solution to this is to negotiate... The sensible thing is to stop the rockets, then the action stops and we can try and find a proper way forward.''
Daniel Taub, the Israeli ambassador to the UK, said Hamas needed to accept ''some basic ground rules'', which meant acknowledging the right of Israel to exist and renouncing violence.
Speaking on ITV's Daybreak, he said: ''Ideally what we want to see is a peace treaty. That's why we have been trying to deal with the Palestinian Authority in Ramallah, where we have been saying 'come to the negotiating table'.
''Unfortunately in Hamas in the Gaza Strip we have a group that is hell-bent on the destruction of Israel.''
Chief Rabbi Lord Sacks issued a plea for ''a continued prayer for peace, not only in Gaza but the whole region''.
Lord Sacks told BBC Radio 4's Today programme: ''No one gains from violence - not the Palestinians, not the Israelis. This is an issue where we must all pray for peace and work for it.''