Senator Richard M. Burr of North Carolina, the committee’s Republican chairman, and Senator Mark Warner of Virginia, the top Democrat, were so perturbed by the leak that they demanded a rare meeting with Speaker Paul D. Ryan last month to inform him of their findings. They used the meeting with Mr. Ryan to raise broader concerns about the direction of the House Intelligence Committee under its chairman, Representative Devin Nunes of California, the officials said.

To the senators, who are overseeing what is effectively the last bipartisan investigation on Capitol Hill into Russia’s interference in the 2016 election, the leak was a serious breach of protocol and a partisan attack by one intelligence committee against the other.

The text messages were leaked just days after the same House Republicans had taken the extraordinary step of publicly releasing, over the objections of the F.B.I., a widely disputed memorandum based on sensitive government secrets. Taken together, the actions suggested a pattern of partisanship and unilateral action by the once-bipartisan House panel.