According to Sky News, Wragg said in the House of Commons that he was extremely displeased with the mini-budget and the current administration's approach to the UK economy.
"I can't go and speak to my constituents, look them in the eye and say they should vote for our great party," Wragg was quoted as saying by the broadcaster.
The lawmaker also said he would not vote against Labour's proposal to ban fracking, as he wished to maintain the no-confidence letter.
Ragg became the sixth Conservative MP to publicly call on Truss to resign, the report said.
The broadcaster noted that Truss canceled her scheduled visit to an electronics company earlier in the day, during which she was due to answer questions from journalists.
A Downing Street source said, as quoted by the broadcaster, that the visit was canceled due to "government business", declining to give further details.
Last week, inews reported, citing lawmakers, that nearly 100 members of the UK parliament had written letters to Brady asking for a vote of no confidence in Truss due to her failed economic policy.
Truss's government has been harshly criticized for its economic policy that proved unable to curb inflation and price hikes, as well as sparked concerns about an increase in public debt. The so-called mini-budget was presented on September 23 by then-Chancellor Kwasi Kwarteng, who had to step down last Friday.
After the plan's announcement, the yield on five-year UK government bonds rose to its highest level since 2008, at 4.6%, which meant a decrease in demand for debt securities. Consequently, sterling fell to an all-time low of $1.054 per pound.
Earlier in the day, Foreign Secretary James Cleverly said that Truss’ resignation would not solve the problems in the country.