WASHINGTON — The special committee scrutinizing the Jan. 6 attack on the Capitol issued three more subpoenas Thursday, turning its focus to organizers of the “Stop the Steal” rally that led into the mob violence.

The subpoenas seek deposition testimony from Ali Abdul Akbar, also known as Ali Alexander, and Nathan Martin, who were involved in organizing the “Stop the Steal” rallies that before the riot spread the lie that there was widespread fraud in the 2020 election. The committee also issued a subpoena for Stop the Steal L.L.C., an organization affiliated with the event.

“The rally on the Capitol grounds on Jan. 6, like the rally near the White House that day, immediately preceded the violent attack on the seat of our democracy,” Representative Bennie Thompson, Democrat of Mississippi and the chairman of the committee, said in a statement. “Over the course of that day, demonstrations escalated to violence and protesters became rioters.”

In the weeks before the attack, Mr. Alexander made repeated reference during “Stop the Steal” events to the possible use of violence to achieve the organization’s goals, and he claimed to have been in communication with the White House and members of Congress regarding events planned to undermine the certification of the 2020 Electoral College results, the committee said.

Mr. Alexander, a far-right activist and conspiracy theorist, has claimed that he, along with Representatives Mo Brooks of Alabama, Paul Gosar of Arizona and Andy Biggs of Arizona, all Republicans, set the events of Jan. 6 in motion.

“We four schemed up of putting maximum pressure on Congress while they were voting,” Mr. Alexander said in a since-deleted video posted online, “so that who we couldn’t rally, we could change the hearts and the minds of Republicans who were in that body, hearing our loud roar from outside.”

Additionally, Mr. Alexander spoke at a rally on Jan. 5 held by the Eighty Percent Coalition at Freedom Plaza in Washington and led the crowd in a chant of “victory, or death,” the committee said.

The committee has now issued 18 subpoenas and it is clear lawmakers are focusing on the funding, planning and organization of the rally that quickly led to violence as rioters stormed the Capitol, where Congress was meeting to formalize President Biden’s election. They chanted “Hang Mike Pence,” threatened to shoot Speaker Nancy Pelosi and forced lawmakers to evacuate the building. About 140 police officers were injured, and several people died in connection with the riot.

The committee said it was trying to get to the bottom of the organizing of the Jan. 6 event, given the conflicting information its investigators have received.

An organization named “One Nation Under God” submitted a permit application in December to the Capitol Police for a rally about “the election fraud in the swing states” on Jan. 6 that listed Mr. Martin’s phone number and email address among the contact information. But when a Capitol Police official spoke with Mr. Martin at the end of December, Mr. Martin claimed not to have any information about the rally and directed the official to speak with a vendor, the committee said. According to the police official, the vendor was “shocked” to learn this because he was in “daily communication” with Mr. Martin about the event, the committee said.

After the Jan. 6 attack, Mr. Alexander released a statement acknowledging that Stop the Steal had obtained the rally permit “for our ‘One Nation Under God’ event,” the committee said. He said it was the intention of Stop the Steal to direct attendees of the rally to march to Lot 8 on the U.S. Capitol Grounds, which is the location for which the Capitol Police granted the permit for the “One Nation Under God” rally. The permit application estimated the event would have only 50 attendees, not the hundreds who marched on the Capitol.

The subpoenas require Mr. Alexander and Mr. Martin to produce documents by Oct. 21 and testify at depositions the next week.

“The Select Committee needs to understand all the details about the events that came before the attack, including who was involved in planning and funding them,” Mr. Thompson said. “We expect these witnesses to cooperate fully with our probe.”

The subpoenas came as time was running out for some of Mr. Trump’s closest allies to comply with the committee’s demands.

Mark Meadows, the former White House chief of staff; Dan Scavino Jr., who was a deputy chief of staff; Stephen K. Bannon, Mr. Trump’s former adviser; and Kash Patel, the former Pentagon chief of staff, had until the end of Thursday to comply with a subpoena to turn over documents to the committee about Mr. Trump’s actions in the run-up to and during the riot.

Mr. Thompson has threatened “criminal referrals” for witnesses who don’t comply with the subpoenas.

The committee is demanding Mr. Meadows and Mr. Patel submit to questioning next Thursday, and Mr. Bannon and Mr. Scavino the following day.

The committee’s latest action came as the Senate Judiciary Committee released a lengthy interim report about Mr. Trump’s efforts to pressure the Justice Department to do his bidding in the chaotic final weeks of his presidency. Mr. Thompson said he planned to incorporate the Senate’s findings into the House inquiry.

“This report has provided alarming details about the lengths to which the former president and his associates went trying to overturn the 2020 election,” Mr. Thompson said.

The committee has also sent record preservation demands last month to 35 technology companies, according to several people familiar with the documents who spoke about their contents on the condition of anonymity. About a dozen House Republicans are among hundreds of people whose records the committee is seeking to preserve, including Representative Kevin McCarthy of California, the minority leader, who has threatened to retaliate against any company that complies.