After the president responded by postponing a trip that Pelosi and other Democrats had scheduled, she obliged by formally rescinding her invitation.
The president then implied that he would seek "alternate" plans, including another venue for his speech.
But on Wednesday evening, he tweeted that he would simply postpone the event.
"As the Shutdown was going on, Nancy Pelosi asked me to give the State of the Union Address." he tweeted. "I agreed. She then changed her mind because of the Shutdown, suggesting a later date. 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," he added in a second tweet.
"I look forward to giving a 'great' State of the Union Address in the near future!" he concluded.
The partial government shutdown has been in effect for 33 days with the president demanding over $5 billion for his promised border wall, and the Democrats refusing to fund any of it.