Prices also ticked upward after the Labor Department reported consumer prices fell short of Wall Street expectations.
Treasury yields fell immediately after the president tweeted his threat, as investors fled for perceived safe haven assets like bonds and gold.
"Russia vows to shoot down any and all missiles fired at Syria. Get ready Russia, because they will be coming, nice and new and 'smart!'" Trump tweeted. "You shouldn't be partners with a Gas Killing Animal who kills his people and enjoys it!"
The yield on the benchmark 10-year Treasury note was lower at around 2.779 percent at 5:26 p.m. ET, while the yield on the 30-year Treasury bond was lower at 2.994 percent. Bond yields move inversely to prices.
Trump's tweet comes in light of a recent chemical weapons attack allegedly carried out by the government of Syrian President Bashar Assad. Trump also criticized Russia's government in a rare rebuke on Sunday, scolding Russian President Vladimir Putin for Moscow's support of Assad.
A senior Russian official on Tuesday threatened to shoot down any U.S. missile that entered Syrian airspace amid rumors that Washington may take military action over the chemical attack.
U.S. consumer prices in the U.S. fell for the first time in 10 months in March, weighed down by a decline in the cost of gasoline. However, underlying inflation continued to firm amid rising prices for health care.
The Labor Department said on Wednesday its Consumer Price Index (CPI) fell 0.1 percent last month, its first since May 2017 and falling short of the Street's expectations for no change.
Excluding the volatile food and energy components, the CPI climbed 0.2 percent, matching February's increase. The so-called core CPI rose 2.1 percent year-on-year in March, the largest advance since February 2017, after increasing 1.8 percent in February.
"Once again, there is a disconnect between wholesale prices and consumer prices," said Kevin Giddis, head of fixed income capital markets at Raymond James. "Right now, there is just enough uncertainty and lower level data to keep the flight to quality bid alive, especially when the President insists on keeping certain conversations alive via Twitter."
The Treasury Department auctioned $21 billion in 10-year notes at a high yield of 2.795 percent. The bid-to-cover ratio, an indicator of demand, was 2.46. Indirect bidders, which include major central banks, were awarded 53.2 percent. Direct bidders, which includes domestic money managers, bought 8.4 percent.
Federal Reserve officials observed an economy growing at a strong pace and inflation moving up at their most recent meeting, justifying continued interest rate increases.
Minutes from the March Federal Open Market Committee meeting revealed that "all participants" expected both the economy to strengthen and inflation to rise "in coming months." The upbeat feeling likely supports the belief that the Fed will continue to hike rates.
"With regard to the medium-term outlook for monetary policy, all participants saw some further firming of the stance of monetary policy as likely to be warranted," the summary stated. "Almost all participants agreed that it remained appropriate to follow a gradual approach to raising the target range for the federal funds rate."