Brodie Clark has also launched a scathing attack on Home Secretary Theresa May whom he accused of making his position "untenable".
In a statement Mr Clark denied "improperly" extending a relaxation of border controls as claimed by Mrs May.
The statement said: "I am anxious to take part in any independent inquiry into matters relating to UK Border Agency.
"But my position at UKBA had been made untenable because of the statements made in the House of Commons by Theresa May.
"Those statements are wrong and were made without the benefit of hearing my response to formal allegations."
The development will increase the pressure on Mrs May, who has insisted she will not resign over the issue.
She is expected to face more questions from MPs on Wednesday after Labour called an Opposition Day debate.
Earlier, Mrs May told MPs she had rejected Mr Clark's proposed changes in favour of a more limited pilot scheme, designed in part to reduce queues at airports.
But Mr Clark went further, scrapping key checks against a Home Office database without ministerial approval, she said. Read More