It’s a goal, not a rule, that bills coming to the House floor have majority Republican support.

“My goal is always to bring bills to the floor that have a strong Republican majority,” Speaker John A. Boehner said at his weekly news conference in response to a question from CQ Roll Call about his willingness to follow the “Hastert rule.”

Conservative outside groups and members of his own party are pressing Boehner to formally embrace a pledge to follow the uncodified rule named for the former speaker to bring bills to the floor that will pass by a majority of the majority party, but the Ohio Republican has resisted that approach. Boehner reiterated on Thursday that he remained confident big-ticket items on the summer legislative agenda would come before the House with robust GOP backing.

That includes the farm bill, he said. At a media briefing on Wednesday, Boehner said he plans to vote for the bill despite some concerns about dairy provisions — and in spite of the fact that many members of the Republican rank and file say $20.5 billion in cuts to the Supplemental Nutrition Assistance Program over a decade does not go far enough.

“There are parts of the farm bill I hope are improved on the floor of the House through an open amendment process,” he said.

As for an immigration overhaul, he continued, “I don’t intend to bring an immigration bill to the floor that violates what I and what my members of my party … what our principles are.”

He didn’t clarify what he meant by that, but it harks back to comments he made earlier in the week on ABC’s “Good Morning America.” Speaking with news anchor George Stephanopoulos, Boehner said that while he didn’t “believe that would be the case,” his approach as speaker could facilitate passage of an immigration bill — and a provision ensuring a pathway to citizenship in particular — without the majority of rank-and-file Republicans onboard.

“I’ve allowed the House to work … well, more than any speaker in modern history, to the point where there are some bills that have passed with a majority of Democrats in favor, and a minority of Republicans,” he said during that interview Tuesday. “And I’ve been criticized for it. What I’m committed to is a fair and open process on the floor of the House, so that all members  have an opportunity.”