The Foreign Secretary also urged Tel Aviv to reduce tension and avoid civilian casualties - but stopped short of demanding an end to its air strikes.
Mr Hague said: "I am gravely concerned by the situation in Gaza and southern Israel and deeply regret the loss of civilian life on both sides. I call on all those involved to avoid any action which risks civilian casualties or escalates the crisis.
"Hamas bears principal responsibility for the current crisis. I utterly condemn rocket attacks from Gaza into southern Israel by Hamas and other armed groups.
"This creates an intolerable situation for Israeli civilians in southern Israel, who have the right to live without fear of attack from Gaza. The rocket attacks also risk worsening the plight of Palestinian civilians in Gaza, which is already precarious.
"Hamas and other armed groups in Gaza should cease attacks against Israel immediately. I call on those in the region with influence over Hamas to use that influence to bring about an end to the attacks.
"I also strongly urge Israel to do their utmost to reduce tension, avoid civilian casualties and increase the prospects for both sides to live in peace. It is imperative to avoid the risk of a spiral of violence. The escalation of the conflict would be in no one's interest, particularly at a time of instability in the region."
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. Citizens in both Israel and Gaza deserve to live in peace and security.
"The recent rocket attacks into southern Israel that have led to this latest response deserve our categorical condemnation but Israel must at all times act in accordance with international law. This latest escalation of violence only emphasises why it is vital that negotiations to achieve a political solution to the Israeli - Palestinian conflict must resume with urgency."