WASHINGTON/BRUSSELS (Reuters) - U.S. Secretary of State Rex Tillerson proposed new dates on Tuesday for a NATO meeting, the State Department said, after he initially decided to skip the talks and rebuffed the alliance’s efforts to reschedule them. Tillerson’s decision to miss his first meeting with NATO foreign ministers, set for April 5-6 in Brussels, unsettled European allies who worried it reopened questions about U.S. President Donald Trump’s commitment to the alliance. Reuters exclusively reported on Monday that Tillerson would stay in the United States to attend Trump’s expected April 6-7 talks with Chinese President Xi Jinping in Florida. U.S. officials also said Tillerson would visit Russia later in April. The alliance had offered to change the meeting dates so Tillerson could attend both it and the Xi talks but the U.S. State Department rebuffed the idea, a former U.S. official and a former NATO diplomat, both speaking on condition of anonymity, said on Monday. On Tuesday, State Department spokesman Mark Toner said the department put forward new dates for a meeting when Tillerson could come, noting that such a decision would have to be made by consensus among the 28 NATO members. “We are certainly appreciative of the effort to accommodate Secretary Tillerson,” Toner told reporters. “We have offered alternative dates that the secretary could attend.” He also sought to allay European concerns by saying that “the United States remains 100 percent committed to NATO.” It was not yet clear if the NATO meeting would be rescheduled to accommodate Tillerson. During his election campaign and on the eve of taking office in January, Trump called the North Atlantic Treaty Organisation “obsolete,” although he has since said he strongly supports the alliance. “No matter how you spin it, this is unfortunate symbolism,” said one senior European diplomat of Tillerson’s plan to skip the April 5-6 NATO Brussels meeting, saying it undid the work of Trump’s vice president and defense minister, who visited NATO headquarters in February to provide reassurances after Trump’s criticism of the alliance. NATO Secretary General Jens Stoltenberg was in Washington on Tuesday. Posing for photographs with Defense Secretary James Mattis, he declined to answer a reporter’s questions on what signal it sent that Tillerson did not plan to attend the meeting, according to a reporter who attended the session.     Some allies, particularly in the former Soviet bloc, are acutely sensitive to any sign of waning U.S. interest in their defense as they deal with a more assertive Russia. Concerns that Trump is too close to Russian President Vladimir Putin, whom the West has sought to isolate for annexing Crimea from Ukraine in 2014, made Tillerson’s expected visit to Brussels all the more pressing, European allies said.  Tillerson worked with Russia’s government for years as a top executive at Exxon Mobil Corp, and has questioned sanctions against Moscow that he said could harm U.S. businesses. “We needed to hear his vision for the alliance,” said a diplomat due to attend the April ministerial meeting. NATO’s quarterly meetings are closed-door sessions over about two days in which governments discuss security strategies and approve top secret documents designed to guide the nuclear-armed alliance in areas ranging from training in Afghanistan to defenses against Iranian missiles. Given the U.S. role as the de facto head of the alliance, it is rare for the country’s top diplomat to miss a NATO meeting. The last time was during the Iraq war in 2003, when Colin Powell was forced to cancel at the last moment. Trump himself is expected in Brussels for a NATO summit in May, although the date is still under discussion. NATO has proposed holding that meeting on May 25, a NATO diplomat said. Several diplomats said they were unhappy that Tillerson had not offered to hold a NATO meeting in Washington later this week, given that most alliance foreign ministers and Stoltenberg will be there for a meeting of an international coalition against the Islamic State militant group. A State Department spokeswoman said on Monday night that all NATO members except Croatia would be at those talks. On Tuesday, Toner said Croatia would in fact attend, saying the department had made “a late night gaffe” and adding, “in no way do we want to diminish Croatia’s valuable role within the alliance.” 