The planned vote sets up a Democratic showdown with Trump's fellow Republicans on an issue dear to the president on the first day of divided government in Washington since he took office in January 2017 with a Congress led by his own party, Reuters reported on Tuesday.
Democrats formally take control of the House from the Republicans after winning a majority of seats in November's congressional elections.
The two-part Democratic package filed on Monday in the House includes a bill to keep funding for the Department of Homeland Security at current levels through Feb. 8 with no new wall funding, as well as a bundle of six measures worth nearly $265 billion combined that would fund the other shuttered agencies through the Sept. 30 end of the current fiscal year.
The two parts will be voted on separately on the House floor on Thursday, said Democrats, who will hold a 36-seat majority.
If approved in the House, the funding package would go to the Republican-led Senate. Its prospects there appear unpromising, although Trump's unpredictability makes it hard to gauge how the shutdown showdown will play out.
"It's simple: The Senate is not going to send something to the president that he won't sign," said a spokesman for Senate Republican leader Mitch McConnell.
The Democratic legislation will mark the first major battle pitting the incoming Democratic House majority led by Nancy Pelosi against Trump and McConnell.
"While President Trump drags the nation into Week Two of the Trump Shutdown and sits in the White House and tweets, without offering any plan that can pass both chambers of Congress, Democrats are taking action to lead our country out of this mess," Pelosi and top Senate Democrat Chuck Schumer said in a joint statement.
Democrats oppose Trump's demand for wall funding, with Pelosi calling the wall immoral, ineffective and expensive.
Democrats hope their two-pronged funding approach will put Senate Republicans in a tough position. If they reject funding for departments unconnected to border security, Republicans could be seen as holding those agencies and their roughly 800,000 affected workers hostage to Trump's wall demand.
"Then they are complicit with President Trump in continuing the Trump shutdown and in holding the health and safety of the American people and workers' paychecks hostage over the wall," Pelosi and Schumer said in their statement.
Non-border-related agencies include the Departments of Agriculture, Interior, Transportation, Commerce and Justice.
The homeland security piece of the package includes $1.3 billion for border fencing and roughly $300 million more for other border security items including cameras and technology.
Democrats said the entire package is based on legislation that has already been passed by either the Senate or Senate committees.
The shutdown, which began on Dec. 22 and has idled roughly a quarter of the federal government, was precipitated by Trump's demand, under pressure from conservative commentators, that Congress approve $5 billion to help fund a wall that was a promise made in his 2016 election campaign, although he said at the time it would be paid for by Mexico.
Trump has called the wall crucial to combating illegal immigration and drug trafficking. The Senate on Dec. 21 failed to muster the votes needed to pass Republican-backed House legislation that included Trump's wall funding. Passage in the Senate would need at least some Democratic support to reach the 60-vote threshold required.