By Arshad Mohammed and John Walcott

WASHINGTON, March 20 (Reuters) - U.S. Secretary of State Rex Tillerson plans to skip an April 5-6 meeting of NATO foreign ministers for a U.S. visit by the Chinese president and will travel to Russia later in the month, U.S. officials said on Monday, a step allies may see as putting Moscow's concerns ahead of theirs.

Tillerson intends to miss what would be his first meeting in Brussels with the 28 NATO members to attend President Donald Trump's expected April 6-7 talks with Chinese President Xi Jinping at Trump's Mar-a-Lago resort in Florida, four current and former U.S. officials said.

The decisions to skip the NATO meeting and to visit Moscow risked feeding a perception that Trump may be putting U.S. dealings with big powers before those of smaller nations that depend on Washington for their security, said two former U.S. officials.

Trump has often praised Russian President Vladimir Putin, and Tillerson worked with Russia's government for years as a top executive at Exxon Mobil Corp, and has questioned the wisdom of sanctions against Russia that he said could harm U.S. businesses.

State Department spokesman Mark Toner had no immediate comment on whether Tillerson would skip the NATO meeting or visit Russia. Two U.S. officials said Tillerson planned to visit Moscow on April 12.

"It feeds this narrative that somehow the Trump administration is playing footsy with Russia," said one former U.S. official who spoke on condition of anonymity.

"You don't want to do your early business with the world's great autocrats. You want to start with the great democracies, and NATO is the security instrument of the transatlantic group of great democracies," he added.

Any visit to Russia by a senior Trump administration official will be carefully scrutinized after the director of the Federal Bureau of Investigation on Monday publicly confirmed his agency was investigating any collusion between the Russian government and Trump's 2016 presidential election campaign.

Trump has already antagonized and worried NATO allies by referring to the Western security alliance as "obsolete" and by pressing other members to meet their commitments to spend at least 2 percent of gross domestic product on defense.

Last week, he dismayed British officials by shrugging off a media report, forcefully denied by Britain, that the administration of former President Barack Obama tapped his phones during the 2016 White House race with the aid of Britain's GCHQ spy agency.

A former NATO diplomat said he hoped there might be a way for Tillerson to attend both meetings, for example by changing the date of the NATO talks.

The former diplomat, who also spoke on condition of anonymity, said it was vital to present a united front toward Moscow. The North Atlantic Treaty Organization was created in 1949 to serve as a bulwark against the Soviet Union.

"Given the challenge that Russia poses, not just to the United States but to Europe, it's critical to engage on the basis of a united front if at all possible," the diplomat said. (Additional Reporting by Jonathan Landay; Writing by Arshad Mohammed; Editing by Lisa Shumaker)

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