The vote was 231-191, with two Democrats siding with Republicans, The Hill reported.
Under the rule, there will be an hour of debate on a motion to accept the Senate-passed spending bill along with amendments to defund the Affordable Care Act for a year and eliminate a new 2.7 percent medical device tax, the Washington publication said.
House members will then vote on the two amendments. If they pass, as expected, the continuing resolution then votes back to the Senate without a final vote.
The rule also provides for 40 minutes of debate and a separate vot on H.R. 3210, which provides continued funding for the military along with related civilian personnel and contractors should there be a government shutdown, The Hill said.
The measure would fund the federal government operations through Dec. 15, rather than through Nov. 15 as the Senate bill calls for.
"Today Republicans in the House of Representatives moved to shut down the government," White House press secretary Jay Carney said in a prepared statement. "Congress has two jobs to do: pass budgets and pay the bills it has racked up. Republicans in Congress had the opportunity to pass a routine, simple continuing resolution that keeps the government running for a few more weeks. But instead, Republicans decided they would rather make an ideological point by demanding the sabotage of the healthcare law."
Carney said congressional Republicans have "tried and failed to defund or delay the healthcare law more than 40 times, and they know this demand is reckless and irresponsible."
"The president has shown that he is willing to improve the healthcare law and meet Republicans more than halfway to deal with our fiscal challenges, but he will not do so under threats of a government shutdown that will hurt our economy.
"Any member of the Republican Party who votes for this bill is voting for a shutdown," Carney said.
The task of avoiding a shutdown is complicated by a desire among conservatives to repeal or delay implementation of the ACA -- commonly known as Obamacare -- which has become tightly woven into negotiations about raising the national debt ceiling limit, The New York Times reported Saturday.
The Senate passed a stopgap spending measure Friday and then adjourned for the weekend. Senate Majority Leader Harry Reid, D-Nev., scheduled members to return at 2 p.m. Monday, leaving the Republican-controlled House scant opportunity at act before the fiscal year ends at midnight Sept. 30.
Reid has repeatedly said a House bill with any provision defunding healthcare reform will not pass in the Senate.
Hard-line conservatives say they won't approve any measure that doesn't delay the healthcare law but Rep. Charlie Dent, R-Pa., said he is trying to find a workable compromise.
"I do not support shutting the government down," Dent said. "I do not support default -- under any circumstances."
In his weekly radio and Internet address Saturday, President Barack Obama said "a group of far-right Republicans in Congress might choose to shut down the government and potentially damage the economy just because they don't like this law."
Reid said Friday the GOP had been "infected by a small destructive faction" that he said was "more interested in putting on a show" than passing legislation.
"We've passed the only bill that can avert a government shutdown Monday night," Reid said Friday after the party line 54-44 Senate vote.
House leaders delayed until next week a vote on their existing proposal after some members complained it only cut spending about $200 billion over the next 10 years. At the same time, it would suspend the debt limit through the end of next year, allowing the government to borrow $1 trillion more.
The controversy has put House Speaker John Boehner, R-Ohio, in the gun sights of both House Republicans and Senate Democrats, The Hill reported.
Conservatives in the lower chamber say Boehner could be out as speaker if he allows funding of the ACA to be included in the debt limit resolution. Reid says Boehner will be responsible for any government shutdown.
Congress and the White House were able to reach a last-second compromise agreement on raising the debt limit in 2011. Sen. Bob Corker, R-Tenn., isn't hopeful the same thing can happen this year.
"Reading the tea leaves is more difficult. I think it is going to be difficult on the [funding bill] and it may be even more difficult on the debt ceiling," Corker said.