Pelosi is citing concerns about whether the hobbled government can provide adequate security, but Republicans are casting her move as a ploy to deny Trump the stage.
Pelosi says that with both the Secret Service and the Homeland Security Department entangled in the shutdown, the president should speak to Congress another time or he should deliver the address in writing.
Trump did not immediately respond to the request and the White House had yet to offer any official response hours later.
The House has passed a Democratic measure to reopen the government through Feb. 8 and provide $14 billion in emergency spending for recent hurricanes, wildfires and other natural disasters.
The bill was approved 237-187 on Wednesday, mostly along party lines, but appears dead on arrival in the Republican-controlled Senate. The White House says President Donald Trump will veto the bill, calling it unacceptable without a broader agreement to address what Trump calls a crisis at the U.S.-Mexico border.
Some Republicans accused Democrats of politicizing disaster aid, noting that the bill put many GOP lawmakers who support Trump's proposed border wall in the position of voting against disaster aid for their own districts.
House Appropriations Chairwoman Nita Lowey said the bill would help families and communities recover from disasters while reopening the government.
The White House says President Donald Trump has signed a bill that will require some 800,000 federal employees to be compensated for wages lost or work performed during the partial government shutdown.
Wednesday's bill signing was closed to the media. The House and Senate had voted to give the workers back pay whenever the federal government reopens.
The shutdown is in its fourth week with no end in sight.
Federal employees received pay stubs with nothing but zeros on them last week. Some posted photos of their empty earnings statements on social media as a rallying cry to end the shutdown.
The shutdown has resulted from a dispute over border wall funding. Democrats remain opposed to Trump's demand for $5.7 billion. They say they'll discuss border security once the government reopens.
New lawmakers who attended a meeting with President Donald Trump at the White House say the conversation was respectful, but none could name progress the talks made toward reopening shuttered government agencies.
Minnesota Democratic Rep. Dean Phillips said Wednesday that the fact that lawmakers of both parties were sitting down and talking with Trump was progress in itself. And New York Democratic Rep. Max Rose said trust was built within members of the group. He said both Trump and Vice President Mike Pence "spent a lot of time" with the Democrats, calling the talks "very sensible discussions that involved listening and speaking."
Phillips said the group was not there to negotiate but "to better understand each other, which I think we did ... and perhaps provide a little bit of daylight through which we can walk."
Seven Democratic lawmakers, including newly elected freshmen, have arrived at the White House ready to ask President Donald Trump to reopen the government while talks continue over border security.
It's the first group of rank-and-file Democrats to meet with Trump during the shutdown, which stretched into its 26th day Wednesday. The White House has been trying to peel lawmakers away from Democratic House Speaker Nancy Pelosi (puh-LOH'-see), but invitations to Democrats earlier this week were declined.
Those arriving Wednesday for the midday meeting in the Situation Room included five freshmen, several of whom did not back Pelosi as speaker. They represent areas where Trump remains popular. They're from a bipartisan group called the Problem Solvers Caucus.
Ahead of the meeting they wrote there is "strong agreement that if we reopen the government, the possibility exists to work together and find common ground."
Trump is seeking $5.7 billion for a U.S.-Mexico border wall, but Pelosi opposes the wall.
The U.S. Department of Agriculture is temporarily reopening an agency that provides resources to farmers and ranchers.
Agriculture Secretary Sonny Perdue announced Wednesday the department has called back 2,500 employees to reopen Farm Service Agency offices on Thursday, Friday and next Tuesday to process existing farm loans and provide tax documents. The office will not process any new applications for loans or trade aid payments.
Perdue says the USDA is examining its "legal authorities" to ensure it's providing services to its customers during the partial government shutdown, now the longest in U.S. history.
The USDA last week announced its feeding programs, including the Supplemental Nutrition Assistance Program, also known as food stamps, will run through February. But if the shutdown extends into March funding will become uncertain.
House Speaker Nancy Pelosi has asked President Donald Trump to postpone his State of the Union address to the nation — set for Jan. 29 — until the government reopens.
The White House hasn't immediately responded to a request for comment about Pelosi's request, which she made in a letter to the president.
Pelosi says the partial shutdown is raising concerns about security preparations for the speech. The California Democrat notes that the Secret Service and Department of Homeland Security have been without funding for almost four weeks.
The annual speech is perhaps the president's biggest opportunity to present his agenda directly to the public.
Pelosi writes that "given the security concerns and unless government reopens this week, I suggest that we work together to determine another suitable date after the government has re-opened."
She's also raising the possibility that Trump deliver the message in writing, as presidents once did.
Congress is planning to skip next week's planned recess if the partial government shutdown continues. And there's every indication it will drag on.
Neither side is showing signs of backing down.
President Donald Trump has told supporters in a conference call that the shutdown will continue, in his words, "for a long time" if it has to.
And Trump contends that people are impressed at how well the government is working.
Democrats remain opposed to Trump's demand for $5.7 billion to build a wall along the U.S.-Mexico border. They say they'll discuss border security once the government has reopened.
An effort by the White House to divide House Democrats fizzled when centrist and freshmen Democrats didn't accept a White House invitation to lunch with Trump on Tuesday.