WASHINGTON — The Republican chairman of the Senate Foreign Relations Committee said on Monday that he was putting a hold on any future American arms sales to a group of Persian Gulf nations in an apparent move to help resolve a bitter dispute between one of those countries, Qatar, and several of its Arab neighbors.

In an unusual letter to Secretary of State Rex W. Tillerson, Senator Bob Corker, a Tennessee Republican who heads the committee, said he would refuse to consent to weapons sales to the gulf nations until the feuding countries worked to end one of the worst political crises among Arab gulf states in years.

The nations, including Saudi Arabia, Bahrain and the United Arab Emirates, cut economic, diplomatic and travel ties with Qatar this month, accusing it of supporting terrorism.

Since then, Mr. Tillerson has tried to help mediate the deepening crisis but has signaled increasing exasperation with the Saudi-led group, first for enforcing a two-week embargo against Qatar without giving the tiny country any specific ways to resolve a dispute, and then on Sunday, after demands were issued, saying that many of them “will be very difficult for Qatar to meet.”