Rex Tillerson | Nicholas Kamm/AFP via Getty Images Tillerson’s message to NATO: Show Trump the money Secretary of State will make his first trip to the alliance’s headquarters in Brussels this week.

U.S. Secretary of State Rex Tillerson, making his first visit to NATO headquarters in Brussels this week, will reiterate Donald Trump's demand that allies ramp up their military spending, a senior State Department official said.

Tillerson's message will echo comments by U.S. Defense Secretary James Mattis, who pressed the spending issue on a visit last month, and may test the patience of allies who are looking for evidence of the Trump administration's professed support for NATO.

So far, they're not getting much.

Tillerson initially declined to attend the spring gathering of NATO foreign ministers, citing a conflict with a visit to Washington by Chinese President Xi Jinping and a planned trip to Moscow. While critics said that Tillerson could have attended the Brussels meeting given that he travels on a U.S. Air Force jet, NATO nonetheless rescheduled the meeting for Friday so that Tillerson could attend.

But even as NATO Secretary-General Jens Stoltenberg has worked aggressively to address Trump's priorities, the White House has not put much focus on NATO and has still not nominated a NATO ambassador.

Briefing reporters ahead of the trip to Brussels, the senior State Department official said that along with the spending demand, Tillerson would press allies to increase NATO's role in counter-terrorism efforts.

NATO allies have formally committed to allocating at least 2 percent of annual economic output for military spending but only five NATO allies — the United States, Greece, the United Kingdom, Estonia and Poland — hit the target in 2016, according to NATO statistics.

"It’s essential that the allies honor their commitment from the last two previous summits to spend 2 percent of their gross domestic product on defense, and of that defense spending, 20 percent needs to go for capacity building, for investment in capabilities and military equipment," the senior official told reporters on Tuesday.

Beyond spending and terrorism, the official said Tillerson "will also be consulting with allies about our shared commitment to improve the security situation in eastern Ukraine, and the need for NATO to continue to push Russia to end its aggression against its neighbors, and to fulfill the Minsk commitments with regard to Ukraine."

Mattis, during his first trip to NATO since joining the Trump administration, said last month that allies would need to increase spending or risked seeing the U.S. "moderate" its support for the alliance. Mattis repeatedly declined to say what consequences might flow from a failure to meet the targets, citing clear efforts by allies to ramp up expenditures.

The senior official refused to speculate on consequences but insisted that the current imbalance in spending was unsustainable.

"Our security environment is getting ... more difficult," the official said. "It’s important for allies to do this for their own security. It’s not like this is a favor to the United States. The purpose of this commitment, is to improve the security for all of us in the transatlantic region. So the idea is for the allies to honor their commitments. We are demonstrating – the president and the secretary — demonstrating that we are doing more than our share."

Relations between the White House and key European allies have been tense at best.

The official added: "The secretary will make the point that it is not sustainable for the United States to maintain a disproportionate share of this burden. He’ll make that point very clear."

Trump administration officials have tried to emphasize their view of NATO's importance, effectively walking back on comments by Trump during his campaign when he called the alliance "obsolete." But relations between the White House and key European allies have been tense at best.

A meeting at the White House earlier this month between Trump and German Chancellor Angela Merkel was notable mainly for its awkwardness and seemed to do little to close the gulf that has emerged between the longtime allies since Trump's election.