Washington DC - Republican presidential candidate Donald Trump said he intends to continue holding outdoor rallies despite the security lapses that led him to only narrowly survive an assassination attempt.

The Secret Service has agreed to "substantially step up" its operations, Trump wrote on his social media platform Truth Social on Saturday.

"They are very capable of doing so. No one can ever be allowed to stop or impede free speech or gathering!!!" he posted.

Trump has not held an outdoor rally since a gunman on a roof tried to assassinate him at a campaign event on July 13 in Butler, Pennsylvania.

A bullet, or a fragment of one, grazed Trump's right ear and left his face streaked with blood as he was hauled off the stage by Secret Service agents.

The attack also left one audience member dead and two other spectators badly injured. The gunman, Thomas Matthew Crooks, was shot dead. Investigators are still trying to determine the motive.

Secret Service director Kimberly Cheatle resigned on Tuesday amid intense pressure from both Republicans and Democrats.

On Friday, Trump vowed to return to the scene of the crime and hold a "big and beautiful rally." He did not say when it would take place.