Oil prices seesawed near unchanged on Tuesday as another batch of weak euro zone data kept demand expectations curbed while supportive U.S. service sector data helped limit losses. Investors and analysts said price consolidation should be expected. They noted that price drops in the session did not threaten multi-month lows posted on Monday and that Brent crude has slid below $100 a barrel from a 2012 peak above $128 a barrel in March. "It has come off a long way, maybe now it's time to consolidate" said Tony Machacek, oil futures broker at Jefferies Bache. Crude futures and equities prices received a lift from an industry report showing growth in the U.S. services sector picked up slightly in May as a gauge of new orders improved. The dollar's strength helped curb oil prices along with news there would be no official statement following a teleconference held by Group of Seven finance ministers to discuss the euro zone debt crisis. The euro fell after Spain's Treasury minister said high borrowing costs mean the country is effectively shut out of the bond market and the European Union should help recapitalize Spain's debt-laden banks. Brent July crude rose 10 cents to $98.95 a barrel by 12:34 p.m. EDT (1634 GMT), having fallen as low as $97.68, staying well above Monday's 16-month low of $95.63. U.S. July crude was up 12 cents at $84.10, having fallen only to $83.31, well above Monday's $81.21 low. Total Brent crude trading volumes lagged U.S. crude turnover, with Britain's celebration of Queen Elizabeth's 60 years on the throne thinning trade. But both Brent and U.S. dealings were under their 30-day averages. EURO ZONE SLOWDOWN Fanning concerns about global oil demand growth, euro zone retail sales fell more than expected in April, sliding by the biggest margin so far this year, the EU's statistics office Eurostat said on Tuesday. In another indication the euro zone is stumbling, purchasing managers indexes (PMIs) from Markit showed all the bloc's major economies are in various states of decline and the vast private economy shrank in May at the fastest pace in nearly three years. U.S. OIL INVENTORIES U.S. crude stockpiles are expected to have slipped last week, a Reuters survey of analysts taken on Monday showed. A drop in stockpiles would snap a string of 10 stock builds reported by the government. The string of increases in crude stocks has left U.S. commercial inventories at their highest since 1990, according to the Energy Information Administration (EIA). Data from the American Petroleum Institute is due at 4:30 p.m. EDT (2030 GMT) on Tuesday, followed by the EIA's report on Wednesday at 10:30 a.m. EDT. IRAN ASSERTS NUCLEAR RIGHTS While the euro zone's debt crisis, sputtering U.S. jobs growth and China's slowing factory sector have hogged the spotlight and pressured oil and other commodities like industrial feedstock copper, the dispute between the West and Iran over Tehran's nuclear program remains unresolved. An embargo on Iranian crude oil by the European Union remains set for July and on Tuesday a source at Turkey's only refiner said the country has steeply cut imports from Iran in May and June as U.S.-led sanctions tighten. An adviser to Iran's supreme leader urged world powers to formally recognize Tehran's nuclear rights in order to bring about a "favorable result" at talks. With the U.N.'s International Atomic Energy Agency (IAEA) and Iran set to hold a second round of talks in Vienna on Friday, a senior U.S. official said Tuesday that Iran was carrying out apparent clean-up efforts at a military site, Parchin, that the IAEA wants to inspect. Robert Wood, acting head of the U.S. mission to the IAEA, also told the IAEA board that Iran had produced enough low-enriched uranium for several nuclear weapons if refined further to high levels. Iran and the six powers - the United States, France, Russia, China, Germany and Britain – will meet for a third time this year in Moscow on June 18-19 after making little progress at their most recent meeting last month.