NATO, the world's most powerful military alliance, is considering naming its new, billion-dollar headquarters in Brussels in honor of the late Sen. John McCain.

The proposal from British Parliament member Tom Tugendhat would be "considered carefully," NATO spokesperson Oana Lungescu said in a statement. "The Secretary-General has tremendous respect for Senator John McCain," she added.

"John McCain – soldier and senator, American and Atlanticist. He will be remembered both in Europe and North America for his courage and character, and as a strong supporter of NATO. My thoughts are with his family and loved ones," Jens Stoltenberg, NATO secretary-general, tweeted on Saturday.

TWEET

The move to name the NATO headquarters comes on the heels of Senate Minority Leader Chuck Schumer's proposal to rename the Russell Senate Office Building in Washington after McCain. However, Schumer's resolution was not immediately embraced by some Republicans. The building is named for Sen. Richard Russell, a Georgia Democrat who staunchly opposed civil-rights legislation and supported racial segregation. Russell, who was also an advocate for the military and poor children, died in 1971 after nearly 40 years in the Senate.

McCain, who was known at home and abroad as America's warrior politician, died Saturday after a year-long fight with brain cancer. The 81-year-old was a naval aviator, prisoner of war during Vietnam, conservative statesman, presidential candidate and strong supporter of the Western alliance.

Read more: Tributes, condolences pour in following Sen. McCain's death

McCain made frequent visits to NATO member countries throughout his political career and frequently criticized Russia's moves to undermine the alliance. He also voiced disappointment with President Donald Trump's handling of the U.S. relationship with NATO partners.