The military is investigating the alleged involvement of 12 of its service members.
Issa and Cummings also have asked Defense Secretary Leon Panetta to provide details of the military investigation by May 8.
Two other congressional committees are looking into the scandal, as well as the Homeland Security inspector general, while the Secret Service and the White House have conducted internal reviews.
On Monday, Homeland Security acting Inspector General Charles Edwards announced his investigation of the incident, saying the "field work is beginning immediately."
The Senate Judiciary Committee questioned Homeland Security Secretary Janet Napolitano about the controversy at a hearing last week. On Tuesday, Sen. Joe Lieberman, an independent from Connecticut who chairs the Senate Homeland Security Committee, and ranking Republican Sen. Susan Collins said they sent Sullivan a letter Monday that also sought answers about what happened.
"We wish to determine whether those events were indicative of a pattern of behavior by agents or officers of the Secret Service and need to be addressed systemically or if they instead constituted an isolated incident warranting action only with respect to the individuals involved," said the letter from Lieberman and Collins.
The U.S. Southern Command expects to finish questioning the 12 military personnel implicated in possible wrongdoing this week before forwarding its findings to military lawyers for review and then to Gen. Douglas Fraser, commanding general of the U.S. Southern Command, a Defense Department official said Monday.
Last week, the Secret Service distributed new rules for its agents on assignment intended to prevent a repeat of such alleged misconduct, according to two government sources familiar with the resulting investigation.
Enhanced Standards of Conduct, the new guidelines given to all Secret Service personnel, make clear that standards of behavior required in the United States apply on missions abroad, the sources said.
Effective immediately, the new standards require detailed briefings before each trip that will include safety precautions and any necessary designations of establishments and areas that are "off-limits" for Secret Service personnel, the sources said.
Also in the new standards, foreigners are banned from Secret Service hotel rooms at all times, except for hotel staff and host nation law enforcement and government officials on official business, according to the officials, and all Secret Service personnel are prohibited from going to a "nonreputable establishment."
The new standards specify that U.S. laws apply to Secret Service personnel when traveling, rendering invalid the excuse that specific activity is legal in the foreign country, the officials said.
In addition, the new guidelines allow moderate alcohol consumption when off duty but prohibit alcohol consumption within 10 hours of reporting for duty or at any time when at the hotel where the protected official is staying, the officials explained.
An additional supervisor from the Office of Professional Responsibility will now accompany the "jump teams" that bring vehicles for motorcades and other transportation, the officials said. Agents involved in the Colombia incident were part of such a jump team.
Allegations of further transgressions by agents have emerged after the initial reports of heavy drinking and consorting with prostitutes last month before Obama arrived in Cartagena.
Recent claims include an account from El Salvador described by CNN Seattle affiliate KIRO as very similar to the Colombia scandal, involving members of the Secret Service and other government agencies.
However, Panetta said last week that his department is not investigating any of its troops over the reported incident in El Salvador, while State Department spokesman Victoria Nuland said Embassy staff in El Salvador were being questioned about the allegations.
The Drug Enforcement Administration also is prepared to look into, "in an appropriate manner and immediately," allegations that it deems "credible" regarding its agents in El Salvador, spokesman Rusty Payne said. But he added that, while the DEA had seen news reports, "we are unaware of any allegations of misconduct."