Environment Secretary Mr Gove said "cutting taxes for folk who earn what MPs earn and what millionaires earn, I think that is wrong".
The worldwide development secretary was eliminated after coming last with 27 votes, 10 fewer than in the second ballot.
There are now two votes due tomorrow - one at lunchtime and one in the evening, as long as none of the remaining candidates decides overnight to drop out of the contest that is - and many commentators are saying that Sajid Javid might do just that.
However, Mr Stewart's camp made clear that if he did form a pact with Mr Gove, it would be the International Development Secretary who would want to remain in the race.
After his elimination, he tweeted that he had been "inspired" by the support he received which had rekindled his faith and belief in politics.
Moments after they came about, Javid wrote: "Delighted to make it through to the final day of MP voting. We can do this!" "You've injected it with real humility, authenticity, and pragmatism".
Boris Johnson won a third successive ballot, with 143 votes.
Mr Hunt, who came second in the second Tory leadership ballot on Tuesday, also said he was best placed to cut a deal with Brussels on Brexit, saying: "We need a negotiator".
Speaking to the BBC's Victoria Derbyshire show, Stewart said they were talking "because it's clear that Boris is going into the last round".
"And the question is 'who is best placed to sit on stage with Boris Johnson, and who is best placed to ask the testing questions that need to be asked?'"
Boris Johnson has topped the ballot in a third round of voting for the Tory leadership, with worldwide development secretary Rory Stewart eliminated from the race after receiving just 27 votes from fellow MPs.
Of the 30 people who voted for Raab on Tuesday, three fewer than the 33 required to progress, Stewart told the BBC he had gained pledges from two of them. Unlike previous rounds, candidates do not have to gain a specific number of votes but the candidate with the fewest supporters will be eliminated.
Following the vote Tuesday night, the survivors faced off in a TV debate on the BBC, which Johnson was initially expected to miss.
Johnson - who is famous for his "gaffs" - managed to avoid a major slip up, but no single candidate stood out.