It was reported that the Tory Skipton & Ripon MP, who became Northern Ireland Minister under Mr Johnson after previously serving as Chief Whip, was at risk of resignation after Work and Pensions Secretary Amber Rudd quit this weekend.
The departure of Ms Rudd - who complained she had seen little evidence Ministers were trying to find an agreement with Brussels on a new Brexit deal - prompted speculation that other senior Ministers might quit.
But Mr Smith wrote on Twitter today: "Media speculation about me doing anything other than continuing to represent & work flat out for Northern Ireland is v wide of mark."
Mr Johnson was today expected to ramp up the pressure on MPs to back a snap General Election or face five weeks of watching the Brexit negotiations from the sidelines.
Parliament was scheduled to be suspended under the Prime Minister's orders, in a move that would suspend all business in the Commons until October 14.
But Mr Johnson will present MPs with a way out of an enforced holiday by giving them another vote on holding a general election before a final decision to prorogue is taken.
An Opposition law, dubbed the Benn Bill after Leeds Central MP Hilary Benn, that would extend the Brexit deadline until January 2020 is expected to receive Royal Assent before prorogation kicks-in but MPs would be thrown out of Parliament almost immediately afterwards and face a nervous wait to see whether Mr Johnson will obey the legislation.