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* Saudi pumps more as Europe, China economy weakens
* Lower oil prices make it easier to apply sanctions
* Congress working to finalize next package in July
By Timothy Gardner and Roberta Rampton
WASHINGTON, June 27 (Reuters) - For most of this year, the threat of tough U.S. sanctions on Iran, the world's third-largest oil exporter, helped push crude oil prices higher and higher, adding a menacing headwind for struggling global economies.
But in the past few weeks, a combination of higher output from Iran's rival Saudi Arabia and economic troubles in China and Europe have pushed oil prices down 25 percent, putting the threat of sanctions back squarely on Iran.
As June 28 approaches - the day the law allows U.S. President Barack Obama to enforce sanctions on countries that do oil deals with Iran's central bank - Washington is revving up efforts to tighten the squeeze on Tehran.
Lawmakers in Congress hope to finalize in July a new package of sanctions aimed at further crippling Iran's oil revenues after international talks in Moscow last week failed to convince Tehran to scale back its nuclear program.
"Thanks to Saudi production increases and the slump in Europe, it appears that we can have our cake and eat it too," said Suzanne Maloney, a senior fellow at the Brookings Institution's Saban Center for Middle East Policy.
"We can exact a painful price on Tehran for its recalcitrance and avoid any blowback to our own economy, at least in the near term," Maloney said.
Countries in the West believe Iran is working on building nuclear weapons, while Tehran has maintained its nuclear program is strictly for civilian purposes.
Iran's oil exports have fallen as much as 1 million barrels per day, worth about $90 million as the sanctions and an EU embargo starting July 1 push its crude customers to seek alternatives, according to industry sources.
Iran, OPEC's second-largest oil exporter, has a reserve fund of $80 billion to $100 billion that can shield its leaders from the drop in revenues, analysts say, but that cushion only pushes sanctions backers to turn up the pressure.
"Enough is enough. It's time to fully implement crippling sanctions on Iran," said Howard Berman, the top Democrat on the House Foreign Affairs Committee.
"We must finish the process of cutting off Iran's access to the global financial system, close loopholes in sanctions on the Central Bank of Iran, and tighten the screws on the Islamic Revolutionary Guard Corps and the regime's energy and shipping industries," Berman said.
Congress wants the White House to push even harder on Iran. Last December, before Obama had even signed off on the banking and oil sanctions, the House of Representatives had already passed two more bills with additional punitive measures to close what lawmakers see as a laundry list of glaring loopholes.
The Senate followed, finally passing its version of the bill in May. The sanctions are designed to crack down on transactions with Iran's national oil and tanker companies, and hamper Iranian banks' ability to transfer funds electronically.
"House and Senate stakeholders are meeting now and comparing preliminary drafts of a final sanctions law," a congressional source said.
To quickly sort out the differences between the two versions, the bill may be ping-ponged "between the chambers" rather than negotiated through a more formal conference process.
"We're trying to see if we can get the House either to largely accept what we put through, or to come to what would be a quick staff conference that would lead us to a final conclusion that we could ratify," said Democratic Senator Robert Menendez, who helped craft the Iran sanctions package.
Some lawmakers want to add provisions to address loopholes they believe may allow Iran to move money through accounts held by others, including from energy companies.
Also in play is a proposed U.S. ban on insurance to oil cargoes, except for those countries that have received exemptions allowing them to continue a lower level of imports.
Menendez said "one or two" new measures may be added, but said he favored quickly moving the existing bill.
"While there's things I'd like to see, I'd be happy to impress upon the Iranians that we're going to continue to ratchet up the consequences," Menendez said.
Obama also has opportunities to crank up the pressure. His administration has granted exemptions to the sanctions to every major buyer of Iran's oil but China. Japan, for instance, got an exemption for cutting purchases for about 20 percent.
In coming months, the administration could push buyers to cut purchases even more, because the sanctions law requires it to update the waivers every 180 days, said Kenneth Katzman, a Persian Gulf expert at the Congressional Research Service.
But to do that, Washington may need Saudi Arabia to keep production near current levels, the highest in decades. And that is no sure thing, given weakening prices. "This probably cannot go on indefinitely," said Brookings' Maloney. (Edited by Russ Blinch and Lisa Shumaker)