Washington (CNN) The State Department scrambled Tuesday to suggest new dates for Secretary of State Rex Tillerson to attend a meeting of NATO foreign ministers after his plan to skip the annual gathering -- but travel to Russia -- came to light.

Tillerson's decision to miss his first NATO meeting but visit Russia a week later plunged his department into damage control, frustrated allies and left analysts scratching their heads at an administration that once again is rubbing Europe the wrong way and raising questions about its commitment to its Western allies.

"Seeing the Chinese, then going to Russia and avoiding NATO in the middle -- it's weird," said one NATO diplomat, referring to Tillerson's travel to China this month and the news that he would head to Moscow next. "It shows that they don't care about NATO. They are not multilateral."

The former US Ambassador to Moscow, Michael McFaul, tweeted in disbelief about Tillerson's decision to skip NATO but go to Russia, saying incredulously that it had to be "fake news." The senior Democrat on the House Foreign Affairs Committee, Eliot Engel of New York, said he "cannot fathom" the decision, which will "shake the confidence of America's most important alliance."

State Department officials originally said that Tillerson had a conflict but that he would see NATO foreign ministers at a 27-nation meeting on ISIS he is hosting at the State Department Wednesday. But after announcing Monday night that his second-in-command, Thomas Shannon, would attend in his place, on Tuesday State officials put forward new dates for the NATO gathering so that the top US diplomat could potentially participate.

The NATO official said rumors started surfacing that Tillerson wasn't coming to the meeting a few weeks ago. Several countries immediately started trying to change the date.

"We said, if this is the case, we should move the date because there is no sense having a meeting without the new US Secretary of State," the diplomat said.

Diplomats surprised

Many were surprised when instead the statement about Shannon was sent out Monday night, the diplomat said. The alternative dates put forward by the State Department Tuesday were seen as a response to criticism about Tillerson's decision not to attend.

"They probably didn't realize how much impact it would have if he didn't go," the diplomat said. "Now that everybody is screaming about him not going, maybe they will realize."

As one European ambassador to the US put it: "To say the least, everyone is in disbelief."

The brouhaha over Tillerson's travel follows an awkward White House visit Friday by German Chancellor Angela Merkel, after which President Donald Trump took to Twitter to blast Germany for not meeting NATO defense spending commitments. That same week, the White House leveled the unsubstantiated and explosive claim that Britain helped former President Barack Obama spy on Trump, a charge that London vociferously denied.

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Tillerson's expected absence at NATO plays into European unease about the Trump administration's attitudes toward the military alliance and the EU amid concern about the President's interest in warmer ties with Russia. Smaller Eastern European countries fear that will happen at their expense, while the continent's larger nations are unsure about the ultimate direction of US policy.

The White House announced Tuesday that Trump will in fact attend the NATO meetings in Brussels on May 25.

"The President looks forward to meeting with his NATO counterparts to reaffirm our strong commitment to NATO, and to discuss issues critical to the alliance, especially allied responsibility-sharing and NATO's role in the fight against terrorism," the White House said in a statement.

NATO announced Tuesday that Secretary General Jens Stoltenberg will meet Trump at the White House on April 12 to prepare for a meeting of NATO heads of state and government on May 25 in Brussels on the "new security environment, including the Alliance's role in the fight against terrorism, and the importance of increased defense spending and fairer burden-sharing."

The April 5-6 NATO ministerial meeting that Tillerson is skipping is held, in part, to prepare for the leaders' summit. Steven Sestanovich, a senior fellow at the Council on Foreign Relations, said the lower-level meeting also has a symbolic importance.

"The real agenda of the ministerial is conveying that the United States is not rethinking its commitment to NATO," said Sestanovich, who also teaches at Columbia University. "So far, the administration has not been able to convey that."

"And because of all the damage that Trump's statements about NATO have done," Sestanovich added, "it's even more damaging for Tillerson to blow off this meeting."

Trump's criticism lingers

The President decried NATO as "obsolete" during the campaign and has been equally dismissive of the EU. Though many of his Cabinet ministers have stressed US support for Europe's major institutions, European diplomats privately point to the stridently anti-European views of White House chief strategist Stephen Bannon and the President's own tweets, such as his recent one about Germany and NATO.

Acting State Department spokesman Mark Toner stressed that Tillerson's decision not to attend the meeting in no way reflects a US change toward NATO.

"The United States remains 100% committed to NATO," Toner said, "President Trump said it in his very first address to Congress. Our commitment to NATO is unwavering and it remains so."

Yet questions remain, said Julianne Smith, a former Defense Department official who is now a senior fellow at the Center for a New American Security. She described confusion among diplomats, as Cabinet officials say "all the right things, making reassuring statements, valuing the transatlantic relationship," at the same time that "no one knows how Trump personally feels and on top of that, they know Bannon disagrees."

Europeans have been pushing for a major foreign policy address from the Trump to clarify his world view, Smith and diplomats said, particularly the White House policy on Russia.

"The fact that Tillerson will give that answer to Putin before he gives it to NATO is not the signal we want to be sending," said Smith. "We have a lot of skittish allies out there. The optics are all wrong, and unfortunately the optics matter."

She added that the situation would likely delight Russian President Vladimir Putin: "This will certainly encourage him because it will signal to him a breakdown in transatlantic resolve."

Trump's presidency has also been blighted by questions surrounding the ties a number of advisers, past and present, have to Russia. US intelligence agencies are also investigating the possibility that the Kremlin sought to influence the US election in Trump's favor through hacking, among others, the Democratic National Committee.

FBI looks at Trump-Russia ties

On Monday, FBI Director James Comey confirmed his agents were probing whether there was collusion between Trump's campaign aides and Moscow.

Tillerson, who was not part of Trump's campaign, also has close ties to Russia, having done major work there as CEO of ExxonMobil. Putin has presented him with Russia's highest award for a foreign civilian, the Order of Friendship.

The State Department's Toner wouldn't confirm Tillerson's trip to Russia, first reported by Reuters, though officials in Moscow have told CNN he may be there on April 12.

Toner noted other opportunities the top US diplomat will have to see NATO foreign ministers, most immediately the anti-ISIS coalition meeting Tillerson will host Wednesday.

State is "certainly appreciative of the effort to accommodate Secretary Tillerson," Toner said. "It didn't fit in, the original dates, given what he wanted to do. But we've gone back with alternative dates now."

The foreign minister's meeting takes place shortly before Chinese President Xi Jinping visits the US for a crucial meeting with the Trump administration.

Tillerson laid the groundwork for the meeting during a visit to Beijing last week. The State Department would not say whether the Xi visit is the reason Tillerson isn't scheduled to attend the NATO meeting.