The public comments were followed by a series of private meetings at which officials were expected to discuss such matters as whether the USA will extend the temporary legal residency status of about 200,000 migrants from Central America who have been allowed to stay in the country without becoming citizens for almost 20 years.
Pence's decision comes several weeks after the president hired his longtime personal attorney, Marc Kasowitz, to handle Russia-related inquiries. Moscow denies meddling in the campaign.
Speaking at the inaugural Conference on Prosperity and Security in Central America today, Vice President Mike Pence announced he will travel to Central and South America in August on behalf of President Trump. Richard Cullen has a long record as a high-profile attorney in Washington, particularly in Republican circles. He represents former FIFA President Sepp Blatter in the corruption probe into world soccer's governing body.
He was also the US attorney for the Eastern District of Virginia during former President George W. Bush's administration. DeLay was not charged.
Aides said the vice president had considered several candidates before settling on Cullen and made his final decision earlier this week.
The Washington Post first reported Cullen's hiring. He launched into a new Twitter tirade against it Thursday morning, calling it "phony" and the "single greatest with hunt in American political history".More news: Track and field: Fireworks, honors in Usain Bolt's farewell in Jamaica
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"They made up a phony collusion with the Russians story, found zero proof, so now they go for obstruction of justice on the phony story", he wrote. He also was part of George W. Bush's legal team during vote recount in Florida during the 2000 presidential election.
Pence has fumbled publicly in the past while addressing the Trump campaign's Russian ties.
But at Thursday night's congressional baseball game, for which lawmakers were practicing when they were fired upon, Pence said the best of America will shine.
Cullen, for what it's worth, is the godfather of one of former Federal Bureau of Investigation director James Comey's daughters.
Trump responded to reports he is personally being investigated for obstruction of justice with a characteristic scorched earth defense: claiming mistreatment of historic proportions and calling into question the probity of his accusers.
The vice president's office said Pence is committed to cooperating in the investigation, and he hired lawyer Richard Cullen so Pence could continue to focus on the administration's goals.