Trump's message asks Hegseth to "use all available funds to get our Troops PAID" on 15 October, when military personnel would see their pay withheld for the first time since the shutdown began on 1 October.
Many US military employees are considered "essential", meaning they must still show up for duty without pay. Some 750,000 other federal employees - about 40% - have been furloughed, or sent home, also without pay.
Furloughed employees are legally supposed to receive back-pay after a shutdown ends and they return to work, but the Trump administration has insinuated this might not happen.
"The Radical Left Democrats should OPEN THE GOVERNMENT, and then we can work together to address Healthcare, and many other things that they want to destroy," Trump posted on Saturday.
Democrats have refused to vote for a Republican spending plan that would reopen the government after nearly 12 days shut down, saying any resolution must preserve expiring tax credits that reduce health insurance costs for millions of Americans and reverse Trump's cuts to Medicaid, the healthcare program for elderly and low-income people.
Republicans accuse Democrats of unnecessarily bringing the government to a halt, and blame them for the knock-on effects caused by the federal work stoppage.
Finding a way to pay for military salaries could help reduce some of the political risk for congressional leaders if the shutdown drags on.
