Andrew RT Davies was speaking to BBC Wales, following a meeting of the 11 Conservative AMs on Monday.
He said it was the "unanimous view of the group" that he should stay, and he had the backing of MPs and activists.
Tory sources had raised concerns about the leadership, after the party lost three AMs in Cardiff Bay on 5 May.
The Conservatives made gains in every previous assembly poll and enjoyed a successful general election in 2015.
Mr Davies said the decision had been "made for me".
"The unanimous view of the group is for me to continue, the MPs have given their view that I should continue, the activists have given their view that I should continue," he said.
"The party chairman has given his view that I should continue.
"I shall continue in the role as long as I feel that there is a role for me to play, but don't be under any illusions if I believe that there is a better alternative who can take can take us forward into other areas, I will hand the baton on."
A former challenger to Mr Davies has said he would have resigned after the party's election result if he had been in charge.
Nick Ramsay said he was happy to back Mr Davies as leader, but if it had been him he would have acted differently.
First Minister Carwyn Jones has said Labour is likely to seek to form a minority Welsh Government, after winning 29 of the 60 seats in the Senedd.
The new assembly is meeting for the first time on Wednesday.
The Welsh Conservative leader has said his AMs have backed him to stay in the role, despite the party's disappointing election result.