WASHINGTON (Reuters) - While he has swallowed a big budget cut and had the White House veto his chosen deputy, Secretary of State Rex Tillerson is avoiding a public conflict with U.S. President Donald Trump over his department's budget, six current and former U.S. officials said on Thursday.

Instead, Tillerson privately resisted a 37-percent budget cut that some White House officials sought and he convinced Trump he needed more time to identify where savings could be made, two current and one former official told Reuters.

As a result, the White House proposed on Thursday a reduction of some 28 percent on U.S. diplomacy and foreign aid.

"Tillerson isn't opposed to cutting the budget at all, but he figured out that he couldn't win head-to-head battles with the president and the people close to him, so he's pursuing a different strategy, arguing that he can't make wise decisions about what to cut until he's more familiar with his department and its budget," said one of the current officials, a State Department veteran.

Tillerson said in Tokyo on Thursday that his department's current spending is "simply not sustainable," and that he accepted the "challenge" Trump had given him.

"He is making a very sensible calculation," said a former U.S. official, noting that Congress, not the president, holds the purse strings and is almost certain to reject many of the administration's proposed cuts. "You state your loyalty to the president, and then you know that you will not actually have to live with the president's budget."

It is not yet clear, however whether Trump and Tillerson have significant policy differences or if he can defend his department against some of Trump's closest aides such as Steve Bannon who want to dismantle parts of the federal government and limit U.S. engagement with the world, said three of the current and former officials.

The former Exxon Mobil Corp CEO has faced multiple challenges in his first weeks as chief U.S. diplomat, including unpredictable policy pronouncements from Trump.

White House officials vetoed Elliot Abrams, Tillerson's choice for deputy secretary, the department's second-highest post, one of the current officials said. With that job still vacant, it has not been possible to fill the department's other senior positions.

Despite that defeat, Michael Anton, a National Security Council spokesman, said the White House holds Tillerson in high regard.

"President Trump has the utmost confidence in the Secretary of State and looks forward to Mr. Tillerson implementing a bold agenda to revitalise American foreign policy," Anton said.

A White House official said Tillerson has had good access to the president, including multiple lunches, dinners and meetings. Tillerson dined with Trump on Monday, the night before he flew to Asia.

Tillerson has kept a low profile since joining the administration seven weeks ago, spending little time with key State Department officials and only holding his first news conference on Thursday in Tokyo.

He has drawn criticism from many State Department officials who believe he has failed to cultivate potential allies in Trump's cabinet and on Capitol Hill.

Chas Freeman, a seasoned diplomat since the Nixon administration, said Tillerson's low-key style might be a survival tactic.

"If he says something, he runs a big risk of getting crosswise with Trump," Freeman said. "This may be a Fabian strategy," referring to the Roman statesman Fabius who defeated the Carthaginian general Hannibal by avoiding frontal conflict.

(Reporting by Arshad Mohammed and John Walcott; Editing by James Dalgleish and Lisa Shumaker)