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Responding forcefully to a letter from the president earlier in the day in which he essentially dared her to disinvite him, Pelosi said in a letter to Trump that the House would not consider a measure authorising the speech for now.
“Again, I look forward to welcoming you to the House on a mutually agreeable date for this address when government has been opened,” Pelosi said in her letter.
In response to the letter, Trump told reporters at a healthcare-related event at the White House that he would respond to Pelosi in a timely manner.
The State of the Union speech, an annual rite in American politics that is typically used by presidents to announce their policy goals for the coming year, has become a hostage to the standoff between Trump and congressional Democrats over his demands for funding for a US-Mexico border wall.
That demand triggered a partial government shutdown on December 22 when some US agencies' funding expired for reasons unrelated to border security or immigration. In discussions about legislation to restore funding, Trump initially signaled support.
Then he changed his stance and demanded that any shutdown-ending measure must contain $US5.7 billion ($NZ8.39 billion) to help pay for a border wall, a demand that Democrats oppose. They have since insisted that the government be fully reopened before they will discuss border security.
Pelosi on January 16 asked Trump to consider postponing the speech because of the shutdown, which has left 800,000 federal workers on furlough or working without pay.
Trump said on Wednesday he planned to deliver the address before the US Congress as scheduled on January 29 in the House of Representatives' chamber, rejecting Pelosi's request.
In an escalation of rhetoric that essentially dared Pelosi to disinvite him, Trump told her in a letter, which the White House released, that he was "looking forward" to giving the speech, an annual event in American politics.
"It would be so very sad for our Country if the State of the Union were not delivered on time, on schedule, and very importantly, on location!" Trump wrote.
In her initial request, Pelosi cited concerns about security for the event, traditionally attended by both houses of Congress, most of the president's Cabinet, the Joint Chiefs of Staff and the justices of the Supreme Court.
House staffers said there has been no preparatory "walk-through," as is customary a few days ahead of the speech, involving security officials and House personnel.
Trump brushed aside security concerns. In his letter, he said the Department of Homeland Security and the US Secret Service had told him there would be "absolutely no problem" with security for the evening address on Capitol Hill.
"Therefore, I will be honoring your invitation, and fulfilling my Constitutional duty, to deliver important information to the people and Congress of the United States of America regarding the State of our Union," Trump wrote to Pelosi. "I look forward to seeing you on the evening of January 29th in the Chamber of the House of Representatives."
Trump sees the border wall as necessary to help stop illegal immigration and drugs from entering the country. Democrats reject the wall as a costly and ineffective step.
Pelosi, speaker since January 3 when Democrats took over majority control of the House, like many other senior lawmakers from both parties has clashed with Trump.
On January 17, the president cancelled a flight Pelosi had been scheduled to take on a US military plane just hours before she and several other lawmakers were set to travel to Afghanistan to visit US troops.