LONDON, Nov 12 (Reuters) - British foreign minister Jeremy Hunt will visit Saudi Arabia and the United Arab Emirates on Monday to press for an end to the war in Yemen and to call on Saudi leaders to cooperate with an investigation into the murder of journalist Jamal Khashoggi.

The visit comes at a time when Riyadh, already under scrutiny for civilian deaths in Yemen air strikes, is facing global criticism and potential sanctions over the murder of Khashoggi at its Istanbul consulate on Oct. 2.

Britain has called for a "credible" investigation into Khashoggi and has pushed for new action at the United Nations Security Council to try to end hostilities in Yemen and find a political solution to the war there.

"The human cost of war in Yemen is incalculable: with millions displaced, famine and disease rife and years of bloodshed, the only solution is now a political decision to set aside arms and pursue peace," Hunt said in a statement.

"So today I am travelling to the Gulf to demand that all sides commit to this process."

The foreign ministry said Hunt would meet Saudi Arabia's King Salman, Crown Prince Mohammed bin Salman, Abu Dhabi Crown Prince Sheikh Mohammed bin Zayed Al Nahyan, Saudi Foreign Minister Adel al-Jubeir, Yemeni Vice President Ali Mohsen and Foreign Minister Khaled Al Yamani.

Hunt, the first British minister to visit Saudi Arabia since the murder of Khashoggi a month ago, will also call on the Saudi authorities to do more to deliver justice and accountability for his family.

"The international community remain united in horror and outrage at the brutal murder of Jamal Khashoggi one month ago. It is clearly unacceptable that the full circumstances behind his murder still remain unclear," he said.

"We encourage the Saudi authorities to cooperate fully with the Turkish investigation into his death, so that we deliver justice for his family and the watching world." (Reporting by Elizabeth Piper Editing by Matthew Mpoke Bigg)