Stephen Crabb, a former Welsh Secretary who is backing Sajid Javid, said “the bidding war is nuts” and should not be taken seriously by party members.
Nominations close in the race on Monday. So far three of the eight Welsh Tory MPs have backed Mr Johnson.
Simon Hart, David Jones and Welsh Secretary Alun Cairns have all backed the former foreign secretary, who has pledged to raise the 40% tax threshold to £80,000 a year.
David Davies is supporting Dominic Rabb, who has called for a 5p cut in income tax, while Guto Bebb has backed Sam Gyimah who told the City AM newspaper pledged reform to taxes to boost economic growth.
Sajid Javid has also reportedly suggested cutting income tax for high earners, while Michael Gove has said he would scrap VAT.
“The Tory leadership tax cut bidding war is nuts,” Mr Crabb wrote on Twitter.
“The candidates shouldn’t makes these promises and members shouldn’t take them seriously.”
He said the contest, triggered after Theresa May announced she would be stepping down, is “not the forum for crafting a sensible tax/spend strategy”.
Glyn Davies told BBC Radio Wales Breakfast With Claire Summers that he would be nominating Andrea Leadsom to ensure she can be on the ballot paper.
He said he could be supporting Jeremy Hunt, but has a “tremendous respect” for Michael Gove and wouldn’t be completely against Boris Johnson.
He told the programme he supports Mr Hunt’s views on abortion. The hopeful told Sky News on Sunday the legal limit for abortion should be reduced from 24 weeks to 12 weeks, saying it was “perfectly legitimate”.
“It’s actually a view that I share,” the Montgomeryshire MP said, cautioning that “any prime minister who has a view, it has to go through cabinet, it has to be approved by parliament”.
The British Pregnancy Advice Service said on Sunday called for Mr Hunt to clarify whether he thought “very young women, who may be more likely to have hidden their pregnancy or taken time to confide in someone about their situation, should become mothers against their will”.