Speaker John A. Boehner is vowing that Oklahoma tornado victims will get relief — but he demurred on when and how the House might act on a bill, and whether his conference would support it.

“We’ll work with the administration on making sure they have the resources they need,” the Ohio Republican told reporters.

He repeated that promise, nearly verbatim, three times to each of the three questions he agreed to entertain from reporters at a leadership press briefing Tuesday morning.

He wouldn’t elaborate on when leaders might introduce a disaster relief package in the wake of the devastating tornado. Nor would he comment on whether sending financial aid to the storm’s victims would be a tough sell to his conference, which in the aftermath of Superstorm Sandy put up a fight against any relief bill that didn’t have significant offsets.

Sen. Tom Coburn, R-Okla., has already said he will demand offsets for disaster relief, a position he’s consistently held through the years.

Boehner wouldn’t permit the three Oklahoma Republicans in attendance — Reps. James Lankford, Frank D. Lucas and Jim Bridenstine — to field reporters’ inquiries.

House Republicans have struggled in the past to stay unified on disaster relief, a struggle that could continue if a relief bill is needed beyond the billions already in disaster relief accounts and doesn’t come with new budget cuts.

During the fight for Sandy relief, the overwhelmingly Democratic New York and New Jersey delegations had no trouble getting support from their caucus peers. It was New York Republican Rep. Peter T. King who famously broke party lines and publicly told fundraisers not to donate any more money to the Republican Party until they agreed to stop stonewalling the relief bill.

On Tuesday morning, though, Boehner appeared determined to divert attention from the politics of what comes next to acknowledgment of the reality of the tragedy. He and other members of Republican leadership — Majority Leader Eric Cantor of Virginia; Majority Whip Kevin McCarthy of California; Conference Chairwoman Cathy McMorris Rodgers of Washington and Conference Vice Chairwoman Lynn Jenkins of Kansas — spoke in somber tones about the American spirit of coming together to mourn, pray and rebuild. Boehner, visibly affected, said he had ordered the House flags to be flown at half-staff.

Lankford, the chairman of the Republican Policy Committee, and Lucas, the chairman of the Agriculture Committee, gave brief remarks on the tragedy that had befallen their home state before the question-and-answer session in which they did not participate.

“Understand,” Lucas said, “we will rebuild, and we in the delegation will work with our fellow Oklahomans to make sure they have the ability to do that.”