Even though Trump said the bill "is the most significant investment in our military and our war-fighters in modern history", Obama's first three defence budgets were larger, when adjusted for inflation, according to Todd Harrison at the Washington-based Center for Strategic and International Studies.
Trump and McCain are engaged in a long-running feud that dates to Trump's 2016 presidential run. As chairman of the Senate Armed Services Committee, McCain was one of the most important voices in passing the vast military spending bill that Trump signed Monday.
The bill also authorizes billions of dollars for military construction, including family housing.
"We will increase the size and strength of our military by adding thousands of new recruits to active duty", he said.
The president continued to praise American armed forces, saying "no one on earth can match the strength of the US military". John McCain (R-Ariz.) at an event on Monday where he signed a defense bill named for the former prisoner of war.
Besides setting policy and spending levels, the bill weakens a bid to clamp down on Chinese telecom company ZTE.
The bill represents a $82 billion funding increase for the Department of Defense over the current period, including a $617 billion Pentagon budget, $22 billion for the nuclear weapons program and $69 billion for USA military efforts overseas.
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Leaders of USA intelligence agencies have said they are concerned that ZTE, Huawei Technologies Co Ltd and some other Chinese companies are beholden to the Chinese government or Community Party, raising the risk of espionage.
There had been concerns Trump might be tempted to slash the number of US soldiers on the peninsula as a cost-saving measure, but the bill prevents that. It allows Trump to waive sanctions against countries that bought Russian weapons and now want to buy US military equipment.
Trump never mentioned Sen.
The NDAA was named in honor of Sen.
McCain tweeted that he was "humbled" that Congress chose to name the bill after him.
There was outrage on social media at Trump's failure to mention McCain, with Howard Fineman, NBC anchor, calling it "petty" and "almost beyond comprehension".