The Queen said King Abdullah of Saudi Arabia "will be long remembered by all who work for peace and understanding" as world leaders marked his death amid renewed protests about the human rights record of his regime.
Prime Minister David Cameron and the Prince of Wales are to fly to Saudi Arabia today to join international figures paying respect to the royal family and flags have been lowered on key public buildings in London.
But the decision to fly them at half-mast has drawn sharp criticism from some prominent politicians over abuses of free speech, women's rights and the country's role as cradle of Islamist extremism.
Abdullah, thought to be aged about 90, died on Thursday after two decades in power in the world's biggest oil exporter. He has been succeeded by his 79-year-old half-brother, Salman.
In a statement to Salman, the Queen - now the world's oldest monarch - said she was "saddened" to learn of the death.
She said: "Your distinguished brother Abdullah had devoted his life to the service of the kingdom and the service of Islam. He will be long remembered by all who work for peace and understanding between nations and between faiths.
"I offer Your Majesty my sincere condolences and I offer my sympathy to the Saudi people."
Mr Cameron said that he was "deeply saddened" and that the ruler would be "remembered for his long years of service to the kingdom, for his commitment to peace and for strengthening understanding between faiths".
But the flags issue drew stinging criticism in the wake of Saudi Arabia's recent public beheading of a woman and a sentence of 1,000 lashes meted out to the creator of an online blog, Raif Badawi.
The leader of the Scottish Conservatives Ruth Davidson condemned the move as "a steaming pile of nonsense".
In a split between two of Ukip's key figures, leader Nigel Farage said it showed "respect for an ally in the war against terror" and that the issue of human rights should be taken up "with the new, not the old king".
But MP Douglas Carswell said officials had seriously blundered and showed "immoral" values far from those of the UK public.
Following the 9/11 attacks on the United States in 2001, the kingdom was criticised as the cradle of a radical branch of Islam which gave birth to al-Qaida. Abdullah eventually cracked down hard on the group after al-Qaida mounted terrorist attacks aimed at toppling the monarchy.
A Department for Culture, Media and Sport spokesman said: "In line with long-standing arrangements, the Union flag is flown at half-mast on Government Buildings following the death of a foreign monarch."