* Islamist militants kill 24 Egyptian police in Sinai
* At least 36 prisoners die in disputed circumstances
* EU diplomats meet to review options
* Saudi Arabia cautions West not to pressure Cairo
By Alistair Lyon and Asma Alsharif
CAIRO, Aug 19 (Reuters) - Suspected Islamist militants killed at least 24 Egyptian policemen on Monday in the Sinai peninsula, where attacks on security forces have multiplied since the army overthrew President Mohamed Mursi on July 3.
Three policemen were also wounded in the grenade and machinegun attack near the north Sinai town of Rafah on the border with Israel, medical and security sources said.
The attack underlined the challenges facing Egypt's new rulers, locked in a struggle with Mursi's Muslim Brotherhood in which at least 850 people have been killed since the security forces opened fire at pro-Mursi protest camps last week.
The authorities portray their campaign as a fight against terrorism. The Brotherhood renounced violence decades ago and denies any links with armed militants, including those in Sinai who gained strength since autocrat Hosni Mubarak fell in 2011.
Mounting insecurity in Sinai also worries the United States because the area lies next to Israel and the Hamas-ruled Gaza Strip, as well as the Suez Canal.
At least 36 Islamists died in government custody on Sunday, in an incident that the Brotherhood described as "murder" and the authorities said was a thwarted jailbreak.
"The murders show the violations and abuses that political detainees who oppose the July 3 coup get subjected to," said the Brotherhood.
The Interior Ministry said 36 Brotherhood detainees had been suffocated by tear gas during an attempted prison breakout near Cairo. A legal source said 38 men had died from asphyxiation in the back of a crammed police van.
Egypt's descent into the bloodiest internal conflict in its modern history is causing global jitters, but no consensus on how to respond has emerged in the West or the Arab world.
European Union diplomats were due to meet in Brussels to review how best to leverage some 5 billion euros ($6.7 billion) of promised grants and loans, looking to apply pressure on Cairo's army-backed government to find a compromise.
DISCORD OVER AID
A senior EU official who asked not to be identified said the United States, Europe and Gulf Arab states had only limited influence on the generals now calling the shots in Egypt.
The United States, an ally of Egypt since it made peace with Israel in 1979, has postponed delivery of four F-16 fighters and scrapped a joint military exercise, but has not halted its $1.55 billion in annual aid, spent mostly on U.S.-made arms supplies.
However, Republican and Democrat U.S. lawmakers, some of them reversing the stances they had espoused before last week's crackdown in Egypt, said on Sunday the aid should be suspended.
"For us to sit by and watch this happen is a violation of everything that we stood for," said Senator John McCain, a former Republican presidential nominee.
Saudi Arabia, another U.S. ally, urged Washington and Europe not to penalise Cairo for its drive to crush the Muslim Brotherhood, whose political ambitions arouse mistrust in several Gulf Arab states, with the exception of Qatar.
Egyptian Foreign Minister Nabil Fahmy sought to pre-empt any attempt to use aid flows as a lever by saying he would look at all such assistance to see "what aid is being used to pressure Egypt and whether this aid has good intentions and credibility".
Hundreds of Brotherhood supporters have been arrested to try to end weeks of protests, but the group has refused to yield, staging rallies in Cairo and Alexandria on Sunday.
The prime minister has proposed disbanding the 85-year-old Brotherhood, which has won all of the five votes held in Egypt since the popular revolt that toppled Mubarak in 2011.
In his first public comments since hundreds of people were killed when security forces cleared two pro-Mursi camps in Cairo on Wednesday, army chief Abdel Fattah el-Sisi said he would not "stand by silently watching the destruction of the country". (Reporting by Cairo bureau; Editing by Peter Graff)