Investors are focused on whether US President Donald Trump and Chinese President Xi Jinping can de-escalate the trade war between the two countries when they meet at the G20 summit in Japan.

Tariffs between the two counties has been blamed on slowing international growth, which has promoted global central banks to adopt looser policies.

"That's one of the biggest uncertainties in the market right now, and has an effect on data and growth," said Justin Lederer, an interest rate strategist at Cantor Fitzgerald in New York.

Benchmark 10-year notes were last up 10/32 in price to yield 2.033 percent, down from 2.066 percent on Friday.

The yields fell to their lowest since November 2016, on Thursday, a day after the Federal Reserve signaled interest rate cuts as early as July to battle growing global and domestic economic risks.

Interest rate futures traders are pricing in a 64 percent chance of a 25 basis point cut in July, and a 36 percent chance of a 50 basis point cut, according to the CME Group's FedWatch tool.

Trump again criticized the US central bank on Monday for not cutting interest rates, keeping up his pressure on the central bank to change its policies.

Rising tensions between the United States and Iran have also boosted safe haven buying of US debt.

Trump said on Saturday he would impose fresh sanctions on Iran but he wanted to make a deal to bolster its flagging economy, an apparent move to defuse tensions following the shooting down of an unmanned US drone this week by the Islamic Republic.

Demand for bonds from investors rebalancing accounts for quarter-end is also expected this week.

The Treasury Department will sell $113 billion in coupon-bearing supply this week, including $40 billion in two-year notes on Tuesday, $41 billion in five-year notes on Wednesday and $32 billion in seven-year notes on Thursday.