President Trump’s lawyers began their promised assault on former Vice President Joseph R. Biden Jr. and his son, Hunter, on Monday, describing what they said was significant evidence of corruption that made Mr. Trump’s interest in the case proper.

Pam Bondi, one of the president’s lawyers, said the defense team would rather have ignored questions about the former vice president and his son, but was forced to address the issue after the House prosecutors referenced the Bidens and a Ukraine energy company more than 400 times.

She accused Democrats of denying the legitimacy of investigations into the Bidens because the House case depends on the premise that Mr. Trump was only interested in the negative political impact of the investigations on his rival.

“They say sham. They say baseless,” Mr. Bondi told the senators. “They say this because if it’s okay for someone to say, ‘hey, you know what, maybe there’s something here worth raising,’ their case crumbles.”

Jay Sekulow, another lawyer for Mr. Trump, had earlier hinted that the defense team would spend significant time on the Bidens after the House managers concluded their arguments. As promised, Ms. Bondi delved deeply into Hunter Biden’s work on the board of Burisma, the energy company, at the time his father was vice president.

At one point, she played a television interview with Hunter Biden.

“If your last name was not Biden, do you think you would have been asked to be on the board of Burisma?” Mr. Biden is asked. “I don’t know. I don’t know. Probably not.”

Democrats say the activities of the Bidens are irrelevant to the president’s actions regarding Ukraine, and insist there is no legitimate evidence that either Hunter Biden or the former vice president did anything improper. They accuse Mr. Trump of trying to smear the elder Mr. Biden because he is a leading candidate for the Democratic presidential nomination.