Last month, Trump threatened 5pc tariffs on Mexican goods, which would have increased every month until they reached 25pc in October unless Mexico stopped the flow of undocumented immigrants across the two countries' shared border. On Friday, the tariffs were called off after an agreement was reached.
Trump on Monday said another portion of the deal with Mexico would need to be ratified by Mexican lawmakers. He did not provide details but warned that if Mexico's Congress did not approve the plan, he would impose tariffs.
The largest gains were at the long end of the Treasury yield curve, with the benchmark 10-year yield up 5.2 basis points to 2.136pc and the 30-year yield up 5.2 basis points to 2.623pc.
That steepened the yield curve, measured as the spread between the two- and 10-year yields, to 24.5 basis points.
"Trump's walking back of potential tariffs on Mexican imports has offered a reprieve, not reversal, of the recent bullish price action in Treasuries," wrote Ian Lyngen, head of US rates strategy at BMO Capital Markets.
"It follows intuitively that positive news on one of the multiple trade war fronts would offset (at least to a small degree) the building economic apprehension which was furthered by Friday's disappointing employment data."
On Friday, the 10-year yield hit its lowest since September 2017 as domestic employers hired far fewer workers than expected in May, raising bets the Federal Reserve would lower interest rates in 2019.
Trading off the US-Mexico deal resolution, two-year yields , which move with market expectations of rate cuts, were higher on Monday, last up 4.1 basis points to 1.890pc.
Using CME Group's FedWatch tool, expectations for a rate cut at the Fed's June meeting fell to 19.2pc from 25pc on Friday.
However, 68.9pc of traders on Monday were predicting a cut at the July meeting, versus 66.3pc on Friday.
The Mexico trade resolution did not fundamentally alter the forecast of multiple rate cuts in 2019, because it does little to inform chances of a deal with China, said Lyngen.
Fed Chairman Jerome Powell said on June 4 that the central bank would respond "as appropriate" to the risks posed by a global trade war, opening the door to a possible rate cut.