Trump also criticised House leader Nancy Pelosi for withdrawing a previous invitation to deliver the address.
The House Speaker said she changed her mind because of the shutdown, which has lasted more than a month and affected 800,000 federal workers.
“This is her prerogative – I will do the Address when the Shutdown is over. I am not looking for an alternative venue for the SOTU Address because there is no venue that can compete with the history, tradition and importance of the House Chamber,” the president said in the tweet.
In a letter to Trump on Wednesday, Pelosi said: “I am writing to inform you that the House of Representatives will not consider a concurrent resolution authorising the president’s State of the Union address in the House chamber until government has opened.”
Passage of such a resolution is required before the president can speak in the House.
The speech had been set for January 29.
Trump had said earlier on Wednesday he planned to deliver the State of the Union address in the House chamber as scheduled, rejecting Pelosi’s request that he delay it.
In an escalation of rhetoric that essentially dared Pelosi to uninvite him, Trump told her in a letter, which the White House released earlier on Wednesday, 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.
Longest shutdown in history
The ongoing partial government shutdown, the longest of its type in US history, came into effect over Trump’s demand for billions of dollars in funding to erect a wall on the US-Mexico border.
Entering into its 34th day on Thursday, furloughed federal employees, unions and others have expressed anger over being forced to work without pay or not being permitted to work at all.
On Saturday, Trump offered to temporarily extend protections for young undocumented individuals brought to the country as children, as well as that of Temporary Protection Status holders in exchange for border wall funding.
Before the plan was officially announced, Democrats decried it as “unacceptable” and “inadequate”, calling it “a compilation of several previously rejected initiatives”.
Conducted between January 18 and 22, a Politico/Morning Consult poll found that only seven percent of voters support “dedicating funding to a border wall if it was the only way to end the government shutdown”.