* Data suggests Saudi exports below 7 mbpd in May, early June
* Saudi said exports especially to U.S. would drop from June
* U.S. buyers taking less after selling price raised - source
* Saudi crude burning to fall this summer - source
DUBAI/LONDON, June 14 (Reuters) - Saudi Arabia's crude exports are expected to fall below 7 million barrels per day this summer, according to industry sources familiar with the matter, and shipping data so far supports those figures.
Saudi Energy Minister Khalid al-Falih said in May shipments were set to drop from June, particularly to the United States, as the top OPEC producer aims to limit supply to help balance the market.
Exports in May, when the kingdom's total production was 9.880 million bpd, averaged below 7 million bpd, three industry and shipping sources told Reuters. Early indications suggest that remains the case this month, one of the sources said.
"I'm only looking at the first week of June, and on the face of it there's not much change," said Roy Mason of Oil Movements, a UK-based firm that estimates supply by tracking tanker shipments.
Indicating lower Saudi exports, he said tanker movements suggested shipments to the United States were "less than would be seasonally normal."
Lower exports could help reduce bloated inventories in the United States, the world's largest and most transparent oil market. High stockpiles have weighed on crude prices.
U.S. oil imports from Saudi Arabia were above 1 million bpd from May-August last year, according to U.S. government data. So far in June, Saudi exports to the United States were below 1 million bpd, according to shipping data and industry sources.
Overall, Saudi exports are set to be lower than last year, when the kingdom shipped about 7.4 million bpd on average from May to August.
This is partly because Saudi Arabia usually burns more crude in power stations at home in the summer months to meet extra demand for power as people rely on air conditioners to deal with temperatures that can reach 50 degrees Celsius.
This year, Saudi Arabia is also leading OPEC and other producers in a pact to cut output, a deal initially due to run during the first half of 2017 and now extended until March 2018.
Under the deal, the kingdom should not produce more than 10.058 million bpd until March. In the first five months of 2017, its output has been below that target.
Industry sources with knowledge of Saudi crude exports data said state oil company Saudi Aramco aimed to cut its exports to the United Sates to below 1 million bpd in June and July.
Aramco has raised its official selling oil prices (OSPs) for its crude to the United States for July, a move seen as discouraging a further buildup in U.S. oil inventories.
"The high-price numbers prompted U.S. refiners to lower nominations," one industry source said.
The company has cut allocations in July to the United States by 35 percent and to Europe by 11 percent in July. Allocations to Asia were cut by some 300,000 bpd.
Reuters shipping data also points to Saudi exports below 7 million bpd in the first two weeks of June, averaging 6.98 million bpd.
Last year, Saudi Arabia burnt 700,000 bpd of crude to generate power in the peak summer months. That figure was expected to fall by about 100,000-120,000 bpd this year, as the kingdom uses more natural gas, one industry source said.
Two sources said Saudi Arabia could draw from inventories to meet local and export requirements if needed. Saudi inventories rose to 267.854 million barrels in March from 264.704 million in February, according to official data.
But the kingdom would still keep crude production and supply within its OPEC target, another source said.
(Editing by Edmund Blair)