"They could have easily made a deal but decided to play shutdown politics instead. #WeNeedMoreRepublicansIn18 in order to power through mess!" he tweeted.
From midnight Friday US time (4pm AEDT), in the absence of an agreed spending plan, federal services began to come to a halt or be scaled back.
Mr Trump tweeted that the Democrats deliberately engineered the shutdown to sabotage the "great success" of his tax cuts and "what they are doing for our booming economy".
However, Mr Trump's tweets, which shift blame to the Democrats, contradict comments he made in 2013 about the government shutdown during the Obama administration.
Mr Trump spoke to Fox & Friends in 2013 and was asked who should be fired during a government shutdown, as shown in a clip posted by Morning Joe.
"Well, if you say who gets fired it always has to be the top," Mr Trump said.
"I mean, problems start from the top and they have to get solved from the top and the president's the leader. And he's got to get everybody in a room and he's got to lead."
Taking a historical view, Mr Trump said that "when they talk about the government shutdown, they're going to be talking about the president of the United States, who the president was at that time."
"They're not going to be talking about who was the head of the House, the head of the Senate, who's running things in Washington," Mr Trump said.
"So I really think the pressure is on the president," he added.
In the wake of the shutdown, essential services and military activity will continue but many public sector workers will be sent home without wages and even serving soldiers will not be paid until a deal is reached to reopen the US government.
Vice President Mike Pence earlier raised the issue of soldiers' salaries after meeting with US military personnel ahead of a three-country tour of the Middle East.
"You have troops headed down range to Kuwait for six months and they are anxious about the fact that they aren't going to get paid right away," he told reporters. "It's unconscionable."
A deal had appeared likely on Friday afternoon, but Democrats accused Republicans of poisoning chances of a deal and pandering to Mr Trump's populist base by refusing to fund a program that protects 700,000 "Dreamers" — undocumented immigrants who arrived in the US as children — from deportation.
The president shelved plans to fly to Florida to celebrate at his Mar-a-Lago estate the first anniversary of his inauguration to remain in Washington to ride out the shutdown.
