Brown and Abdullah are understood to have discussed Abdullah's 2002 Arab Peace Initiative, which calls on Arab countries to make peace with Israel if the Jewish state withdraws from Palestinian territories.
 
Brown said no date has been set for a US-sponsored Middle East peace conference due to take place in Annapolis, Maryland, but said Saudi Arabia's participation at the meeting is key.
 
Royal meeting
 
Abdullah's meeting with Brown came a day after the king attended a banquet hosted by Queen Elizabeth II at Buckingham Palace.
 
"I am confident we will find from the government of your majesty every help to end the tragedy suffered by our Palestinian brethren through genuine peace that can protect the rights of all parties," Abdullah said during the event.
 
Before the Saudi king arrived in London on Monday, he criticised Britain for not being pro-active enough in fighting terrorism.
 
He accused Britain of failing to act on intelligence that might have prevented the 2005 London transport bombings, in which four suicide bombers killed 52 people.
 
British officials insist they would have acted on firm evidence if it existed, and said the Saudi supplied information was too general.
 
Arms controversy 
 
The countries' relationship had already attracted controversy in recent months over alleged illegal payments made as part of an armaments sale.
 
The king's state visit has been criticised by
human rights activists and politicians [AFP]
The British government stopped an investigation by Britain's Serious Fraud Office in December into whether a Saudi prince received illegal commissions in a $62bn deal with BAe Systems, a British weapons manufacturer.
 
Tony Blair, Britain's prime minister at the time, said the SFO investigation would jeopardise Saudi co-operation in fighting terrorism and cost Britain jobs.
 
The hospitality shown to Abdullah has drawn protests from critics who say the oil-rich kingdom should be condemned for alleged human rights abuses.
 
Vince Cable, acting leader of the opposition Liberal Democrats, boycotted Abdullah's visit and politicians from Brown's Labour party planned a protest outside the Saudi embassy for late Wednesday.