"You can see clearly whether there's any word of conspiracy in that statement. I don't think so," he told a news conference in reference to an NSC statement this month which had expressed concern over non-diplomatic language used in a cable from a "foreign country", widely assumed to mean the United States, about the no-confidence vote.
Pakistan's lower house of parliament eventually voted in favour of removing Khan from office on Sunday.
Opposition parties and analysts say the military helped Khan win election in 2018, which they both deny, but that support waned after a falling-out over the appointment of the country's next intelligence chief late last year.
Khan's former information minister, Fawad Chaudhry, called for the setting up of a judicial commission to probe into the accusation that the United States conspired to topple Khan.
Iftikhar denied Khan's assertion that the army chief of staff, General Qamar Javed Bajwa, had offered to help mediate in his deadlock with the opposition.
Instead, he said, Khan had asked Bajwa to convey to the opposition on his behalf that he would call snap elections if the no-confidence motion was withdrawn.
"(Bajwa) went to the opposition and placed this request in front of them, and after a detailed discussion they said that they wouldn't take any such step, and that 'we will go on as we have planned'," said Iftikhar.
He also clarified that the United States had never asked for military bases in Pakistan after US-led forces' withdrawal from Afghanistan last August. Khan's party had said that Washington turned against him after he said "absolutely not" in a TV interview in response to a question whether he would give the bases to the Americans.
Khan has aired the conspiracy allegations in his public rallies, demanding snap elections.
The next parliamentary election is due in 2023.