* Asia share markets mostly firmer, Nikkei flat as yen seesaws
* Oil prices firm ahead of White House call on Iran deal
* Relief on US wages data tempered by emerging market strains
* Dollar uptrend pauses, supported by outlook for Fed hikes
By Wayne Cole
SYDNEY, May 7 (Reuters) - Most Asia markets firmed on Monday after a tame reading on U.S. wages lessened the risk of faster rate hikes by the Federal Reserve, although Sino-U.S. trade tensions and a looming deadline for an Iranian nuclear deal lurked in the background.
Energy shares were on a roll as oil prices hit their highest in more than three years amid strains in Venezuela's output and talk of possible new U.S. sanctions against Iran.
President Donald Trump has set a May 12 deadline for Europeans to "fix" the deal with Iran over its nuclear program or he would refuse to extend U.S. sanctions relief for the oil-producing Islamic Republic.
Brent crude futures added 76 cents to $75.63 a barrel, while U.S. crude climbed 64 cents to $70.36 to finally crack the $70 barrier.
The week ahead also has important readings on the health of the Chinese economy, and hence global demand, as well as the latest data on U.S. consumer price inflation.
MSCI's broadest index of Asia-Pacific shares outside Japan put on 0.2 percent, while Chinese blue chips rose 1.2 percent.
E-Mini futures for the S&P 500 inched up 0.36 percent and spread betters pointed to opening gains for the European bourses. Japan's Nikkei was flat, recouping losses as the yen shed its early gains.
Friday's U.S. jobs report showed unemployment dropping to a new cycle low of 3.9 percent yet wages remained benign, suggesting the Federal Reserve would keep raising rates but at a gradual pace.
That outlook cheered Wall Street where the Dow ended Friday up 1.39 percent, while the S&P 500 rose 1.28 percent and the Nasdaq 1.71 percent.
Apple Inc hit a record high after Warren Buffett's Berkshire Hathaway Inc disclosed that it had raised its stake in the iPhone maker.
The recent run of solid U.S. economic news contrasts with a softer turn in European data and lifted the dollar to its highest for the year so far against the euro.
The single currency was last at $1.1957, having been down as deep as $1.1911 on Friday. The dollar also reached its highest since December against a basket of currencies and was last trading at 92.609.
It had less luck against the Japanese yen, in part because strains in emerging market currencies were supporting safe havens such as the yen. The dollar steadied at 109.14, having topped out around 110.05 last week.
"It's this recovery in the U.S. dollar – one based on the data flow in the U.S. against the rest of the world – which is catching many by surprise and causing ructions across emerging markets," said Greg McKenna, chief market strategist at CFD and FX provider AxiTrader.
Markets from Argentina to Turkey have been under intense pressure, in part because many of these countries have large amounts of U.S. dollar debt which gets more expensive to finance as the currency rises.
A firming U.S. dollar has also been negative for some commodities, with gold falling for a third straight week before bouncing slightly on Monday to $1,315.12 an ounce.
(Editing by Sam Holmes & Shri Navaratnam)